UC-NRLF 


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LIBRARY 


UNIVERSITY  OF  CALIFORNIA. 


JAN  12    1893  .  iS<> 


Accessions  No. 


Ctes  Ato. 


ENGINEER'S  OFFICE,  CHESAPEAKE  AND  OHIO  RAILROAD,    ) 
RICHMOND,  March  29,  1872.          y 

MAJOR  HOWARD  lias  given  in  this  book  a  simple,  yet  perfectly  accurate 
method  of  ascertaining  the  solid  contents  of  any  prismoid .  The  calculation 
from  end  areas  is  corrected  by  tables  well  arranged  and  few  in  number,  and 
he  has  all  the  accuracy  of  the  prisrnoidal  formula  with  scarcely  more  trouble 
than  in  averaging  end  areas. 

H.  D.  WHITCOMB, 
Chief  Engineer  Chesapeake  and  Ohio  Railroad. 

E.  T.  D.  MYERS, 
,  Chief  Engineer  Richmond,  Fredericksburg,  and  Potomac  Railroad. 


EARTHWORK    MENSURATION, 


OK   THE   BASIS   OP   THE 


PRISMOIDAL    FORMULA. 


CONTAINING  A  SIMPLE  AND  LABOR-SAVING  METHOD  OF 

OBTAINING  PRISMOIDAL  CONTENTS  DIRECTLY  FROM  END  AREAS. 

ILLUSTRATED  BY  EXAMPLES, 

AND  ACCOMPANIED  BY  PLAIN  RULES  FOR  PRACTICAL  USE. 


CO  1ST  WAY    R.     HOWARD, 

CIVIL  ENGINEER,  EICIIJIOND,  VA. 


UNIVERSITY 


NEW  YORK  : 
B.     VAN    KOSTRAim     PUBLISHER, 

23  MURRAY  AND  27  WARREN  STREET. 

1874. 


V 


.V 


Entered,  according  to  Act  of  Congress,  in  the  year  1874,  by 

D.  VAN  NOSTRAND 
In  the  Office  of  the  Librarian  of  Congress,  Washington,  D.  C. 


PREFACE. 


THIS  work  claims  to  present  a  new  and  systematized  method  of 
finding  the  prismoidal  contents  of  Earthwork  by  means  of  Tables 
accompanied  by  Rules  so  plain  and  simple  of  application  as  to  fit  it 
for  the  .common  uses  of  Engineers. 

When  the  ratios  of  the  side  slopes  are  constant  between  end  sec 
tions  of  which  the  transverse  surface  lines  are  sensibly  similar,  all 
ordinary  cases  of  thorough  cut  and  fill,  terminal  pyramids,  side-hill 
work,  and  borrow  pits  are  covered  by  Formulae  (17),  (18),  and 
(19),  and  the  prismoidal  contents  for  all  side  slopes  and  bases  are 
taken  from  Tables  4  and  5  by  Rules  (1),  (2),  and  (3). 

In  the  method  used,  the  heights  of  equivalent  level  sections  are 
not  involved,  nor  is  any  calculation  needed  for  100-feet  lengths 
beyond  ascertaining  the  half -sum  and  the  difference  of  two  quanti 
ties.  For  the  most  part  Tables  do  the  work  of  the  calculator,  and 
any  one  who  can  approximate  cubic  contents  by  the  rough  method 
of  "Average  Areas"  is  competent  to  obtain  the  prismoidal  contents 
by  the  Rules  given. 

The  tables  of  level  cuttings  are  not  needed  when  areas  are  given, 
and  are  included  chiefly  for  use  in  preliminary  estimates  when  the 
only  data  are  the  centre  heights  and  the  angles  of  the  transverse 
surface  slopes.  With  these,  the  heights  of  equivalent  level  sec 
tions  are  readily  found  by  Mr.  Trau  twine's  well-known  and  very  inge 
nious  diagrams,  than  which  for  the  purpose  intended  probably  no  bet 
ter  means  can  be  devised.  When  these  heights  have  been  ascertained, 
the  use  of  the  special  Correction  Tables  in  connection  with  those  of 
level  cuttings  will  reduce  to  a  minimum  the  labor  of  computing 
the  prismoidal  contents.  If  further  tables  of  level  cuttings  are 
considered  necessary,  the  reader  is  referred  to  Mr.  Trautwine's 
"  Excavation  and  Embankment,"  or  to  the  example  given  at  the 
end  of  this  work,  by  careful  attention  to  which  any  required  table 
may  be  written  out  with  entire  accuracy  in  a  few  hours.  Special 
corrections  for  any  side  slopes  may  be  obtained  by  Rule  12. 

Not  an  inconsiderable  advantage  of  the  present  method  is  that,  by 


giving  accurate  corrections  for  the  familiar  approximations  in  gene 
ral  use,  the  calculator  has  the  element  of  error  constantly  before 
him,  and  must  speedily  learn  by  practice,  if  not  by  theory,  the  cases 
in  which  such  corrections  become  important.  But  while  enough  is 
given,  both  by  rule  and  example,  in  Part  II.  to  guide  the  least  theo 
retical  in  the  use  of  the  tables,  in  Part  I.  a  strictly  mathematical 
investigation  of  principles  and  derivation  of  formula  is  submitted 
to  the  careful  reader. 

The  article  on  Correction  of  Contents  for  Curvature  was  sug 
gested  by  that  on  the  same  subject  in  "  Henck's*  Field-Book,"  but, 
by  the  formulae  and  table  of  factors  given,  in  ordinary  cases  the 
corrections  are  much  more  readily  obtained  in  practice. 

All  of  the  tables  in  this  work  have  been  calculated  by  the  writer, 
and,  as  the  system  used  was  that  of  continued  additions  with  special 
tests  at  intervals,  it  is  believed  that  they  will  be  found  absolutely 
correct  within  the  purposed  limits,  whether  the  last  figure  of  any 
amount  given  be  intended  to  express  the  nearest  whole  number  or 
the  nearest  decimal. 


NOTATION  AND  SIGNS  USED. 


A  and  A'  =  end  areas  of  earthwork. 

M  =  middle  area. 

a  and  a'  =  areas  of  triangle  between  road-bed  and  intersec 
tion  of  side  slopes  produced. 

1}  and  y  —  road-bed  widths. 

c  and  c'  =  centre  heights  of  profile. 

li  and  h'  =2  heights  of  equivalent  level  sections. 

s  and  s'  =  ratios  of  opposite  side  slopes  to  1. 

d  and  d'  =  side  distances. 

7ii  and  liz  =  side  heights. 

N,  N',  n  and  ri  =  correction  numbers. 

C  =  contents  for  100  feet. 

Q  =  correction  for  curvature. 

<£>  =  "greater  or  less  than." 

~  =  "the  difference  between." 

"  Grade  triangle  "  =  triangle  between  the  base  and  the  inter 
section  of  the  side  slopes  produced. 


UNIVERSITY 


PART  I. 

AREAS. — GROUND   SLOPING   TRANSVERSELY.       THOROUGH-CUT. 

Fig.   1. 


Let  area  ABCFD  —  A,  area  DFG  =  a,  centre  height  BE  —  c, 
side  heights  AK  and  CL  z=  /^  and  7/2,  side  distances  AM  and  XC 
=  d  and  d',  base  DF  =  5,  and  ratios  of  side  slopes  to  1  =  s  and  s\ 

CASE  1. — Side  slopes  the  same.  6-'  =  s.  Produce  the  side  slopes 
until  they  meet  in  G. 

=  |,  hence  EG  =~ 

2  2s 


,                         xs      b' 
and  area  a  z= —  — 

2  4:3 

But  BG  —  e  -j-  — ,  hence 
area  ACG  —  A  -}-  a  — 


and  A  =  x — 


is 


(1) 


8 

Example.—  Given  s'  —  s  =  f  ;  I  =  18  ft.  ;  d  =  30.9  ;  tf'  =  21.6  ; 
c  =  22.0. 


(tab.  1)  =  12,  and  «  (tab.  2)  =  103. 


and  A  =  892.5  —  108  =  784.5. 
CASE  2. — Opposite  side  slopes  unequal,    s'  <£>  s. 
The   areas  of  the  triangles  DAE,  EAB,  BCE,  and  ECF  arc 
respectively 

-*  X  7i  -  X  h. 

1. £_£*£*£  and? - 

222  2 


and,  A  =  -  — £-  - , (2) 

Example.— s  =  J  ;  6-'  =  1  ;  &  =  1C  ;  c  =  12.6  ;  d  &  d'  =  10.1  & 
20.8;  At  &//8  =  8.4 & 21.8. 

8  (8.4+ 21.8)  +  12.6  (10.1+29.8) 

A.  nr  —  —  "=.  o/U.o. 


CASE  3.  —  DE  greater  or  less  than  EF. 

Let  DE  =  |,  and  EF  =  ^ 

/C  /i 

The  triangles  DAE,  EAB  and  BCE  have    the    same  expressions 
for  their  areas  as  in  case  2,  and  area  ECF  =  ^-X^2 


hence,         A  =  —  .....................  (3) 

/v 

Example.  —  Double  width  track,     s  —  -  ;  s'  =  -  ;  -  =  9  ;  —  =21 

c  =  32.8  ;  7/.J  &  7/8  =  2-4.4  &  40.4  ;  d  &  d'  =  21.2  &  51.3 
A    _  9.0  x  24.4  +  21.0  x  40.4  +  32.8  (21.2  -f  51.3)  _      ' 

~2~ 

Formula  (1)  applies  only  to  case  1  ;  formula  (2)  to  cases  1  and  2  ; 
and  formula  (3)  is  general  for  all  cases  where  the  whole  road-bed 
width  is  either  in  cutting  or  embankment,  and  the  surface  slopes 
are  sensibly  regular  between  the  centre  and  side  stakes. 

AREAS.  —  SIDE   HILL   CUTTING. 

Let  q  —  the  horizontal  distance  from  centre  line  to  grade  point 
opposite,  and  A  =  the  area  of  excavation. 


9 


CASE  1. — Both  centre  and  side  height  in  excavation. 
The  areas  of  triangles  DAE  and  EAB  are  as  before,  and  that 

of  the  triangle  running  out  to  grade  =  ~ 


hence, 


A  = 


2 


Example.—  8  =  1,  1)  —  20,  c  —  4.3,  7it  =  10.G,  d  =  20.6,  and 
q  =  6.2. 


A  = 


1Q  X  10.6  +  4.3  (20.6  +  6.2) 


CASE  2. — Centre  height  in  embankment. 


A  = 


(5) 


Example. — It  =  IS,  li  •=.  10,  q  =  5.     A  = 


(9—5)  10 


=  20 


AREAS. — GROUND  LEVEL  TRANSVERSELY. 

Fig.  2. 

^ ? , S. 5 7B 


G  D 

CASE  1. — Side  slopes  the  same,  or  s'  =  s. 

AE  =  FB  =  7/«,  and  EF  =  CD  -  b 


Area  ABCD  = 
or  A  =   5 


Example.—      s'  =  s  =  -  ;  I  =  16  ;  7i  =  20 

A  =(  16  -}-  20  x  5)20  =  26  x  20  =  520. 


(6) 


When  the  field  notes  are  given,  this  example  can,  of  course,  be 
worked  by  any  one  of  formulae  (1),  (2),  or  (3). 

CASE  2. — Opposite  side  slopes  unequal,  or  s'  <£>  s. 
AE  =  Us ;  FB'  =  Its' ;  and  EF  =  CD. 

His  4-fl  +  /tsf-f  fly 


area 

or    A  = 


AT^rrr^          /AB'-fCD\7         ( 

AB'CD  =  I ^ \h  —( 


li 


10 


Example.— -s  =  - ;  s'  =  1  ;  I  =  16  ;  li  =  20. 

/v 

A  =  (l6  -f  20  x  |)2b  =  31  x  20  =  G20. 

AREAS. — GROUND    BROKEN   TRANSVERSELY. 
Fisr.  3.  • 


To  calculate  the  area  tibcdefy  I'c'd'e'f'y. 

The  elevations  and  horizontal  distances  apart  of  the  points 
a,  I,  c}  d,  c,  ff  fff  must  be  determined  in  the  usual  manner  before 
the  surface  is  disturbed,  and  of  V,  c',  d',  e',f,  (/',  after  the  excava 
tion  is  made. 

Calculate  the  area  Aalcd  efg  B  between  the  surface  line  and 
the  assumed  datum  plane  AB  ;  also 

The  ttre&Aab'c'd'e'f'g'g'B  between  the  bottom  of  the  pit  as 
excavated  and  the  same  datum  plane  AB. 

The  difference  between  the  results  so  obtained,  gives  the  area 
required. 

"When  the  cross  sections  of  the  line  have  the  surface  broken 
transversely,  if  the  slope  stakes  are  supposed  to  be  at  a  and  g  (fig. 
3),  and  AB  is  the  plane  of  the  road-bed,  calculate 

1st  :  the  area  A  a  l>  c  d  cfg  B 


2d  :  the  triangles  of  excess  = 


The  difference  between  the  above  two  results  will  give  the   area 
of  earthwork  required. 

For  side  hill  work  the  process  is  similar,  except  that  only  one 

7i*s 
triangle  of  excess  =  -^-,  is  to  be  deducted. 


11 


This  of  course  applies  to  embankment  as  well  as  excavation. 
Rone  of  the  preceding  cases  require  that  the  cross  section  shall 
be  drawn  before  calculating  its  area, 

CONTENTS.— FRUSTUM  FORMULA. 

Fig.  4. 


If  ABCD  and  A'B'C'D'  bo  two  consecutive  cross  sections  with 
like  surface  lines  and  side  slopes  but  unequal  bottom  widths,  by 
producing  the  side  slopes  until  they  meet  at  E  and  E',  the  whole 
figures  ABE  and  A'B'E'  are  similar  as  well  as  the  triangles  CDE 
and  C'D'E'.  But  the  solid  ABCDA'B'C'D'  being  the  difference 
between  the  frustums  ABEA'B'E'  and  CDEC'D'E'  its  cubic  con 
tents  are 


(ABE  +  A'B'E'  +  VABE  x  A'B'E' 

( 


-     CDE  +  C'D'E'  -f 


x  C'D'E' 


in  which  I  represents  the  distance  between  the  cross  sections. 


12 

If  areas  ABCD,  A'B'C'D',  CDE  and  C'D'E'  be  represented  by 
A,  A',  a  and  a'  respectively,  then  taking  I  as  100  feet,  and  repre 
senting  the  contents  in  cubic  yards  by  C,  we  have  : 

(A+^+(A'+^)+V(A+a)(A'+g')-(^+a'-fV^?)vx100 

~~3~  ~27'( 

If  CD  =  C'D'  then  a'  =  a,  and  the  formula  becomes  : 


a)(A.!+a)         \  100 
*/2f 


When  CD  =  C'D'  =  0,  a  vanishes,  and 
'A.  -f  A'  -f  v'AAA  100 


0  =  1— 


3 


(10) 


which  is  the  formula  for  the  frustum  of  a  pyramid. 

By  formulae  (8),  (9),  and  (10)  the  whole  of  the  formulae  for  cubic 
contents  hereafter  given  may  be  conveniently  tested. 

As  the  solid  resulting  from  connecting  the  homologous  sides  of 
two  similar  and  parallel  sections  of  unequal  areas  is  the  frustum  of 
a  pyramid,  formula  (10)  is  applicable  to  any  plane  solid  with  such 
end  sections, 


CONTENTS. — PRISMOIDAL  FORMULA. 
Fig.  5. 

J? 


Let  ABCDF  be  a  given  cross  section,  with  a  base  FD  =  b,  and 


13 

and  s'  the  ratios  of  its  side  slopes  to  1 ;  also  let  IKDF  be  an  equiva 
lent  cross  section  with  level  surface,  height  MN  =  h,  and  with  same 
base  and  side  slopes.  Produce  the  side  slopes  to  their  intersection  at 
E,  and  from  E  let  fall  the  perpendicular  EL  on  IK,  intersecting  the 
base  in  G.  Let  area  ABCDF  =  IKDF  =  A,  and  FDE  =  a. 

In  the  triangle  FDE,  FG  =  EG  x  s,  and  GD  =  EG  x  *',  or 
FD  =  EG  (s  -f  s')}  whence  EG  =  — ?L   =  _J        anci  arca 

*      *        "  t>if  o    i     t- ' 

<S  -f-  o  6  -j-  o 

__  FDxEG  _  I      _b_  I* 

~~       ~     X        ~ 


s'      2(s  +  sf 
Similarly  in  triangle  IKE,  EL  =  h  '-\- 

IK= 

consequently, 


from  which, 

EL  =  II+—T—-- 


For  convenience  of  calculation,  let  GE  =  --  -.  be   represented 

s-fs' 


A    T7T     1        TT        ^1  S 

by  ff,  and  J.L  by  II  ;  then  as  ^-^  =    --       --  =/-r 

we  have,  by  substitution  in  (11), 


For  a  second  section  with  corresponding  parts  V,  H',  s  and  s'9  and 

areas  A'  and  a' 


and  for  the  area  M  of  a  cross  section  midway  between  A  and  A', 


The  prismoidal  formula  for  the  contents  0  between  two  end 
areas  A  and  A'  at  a  distance  apart  =  I,  with  an  area  M  midway  be 
tween  them  is  : 


14 


But  ^±—  =  ^p.  - 

and  by  substitution  in  (13) 

C  =  M+A'    _A+A'-2MV, (u) 

also  — -—  =  M  -  — t—  ;  and  substituting  this  ku(13) 

C  =  /M+^+4lL 


The  two  last  expressions  for  the  value  of  C  shew  that  the  calcula 
tion  of  contents  by  averaging  the  end  areas  requires  a  minus  correc 
tion  ;  and  by  the  middle  area  (or,  what  is  equivalent,  taking  the 
amount  corresponding  to  the  average  of  the  end  heights  from  a 
special  table)  a  plus  correction  of  exactly  half  as  much.  The  actual 
minus  correction  will  now  be  found.  By  substituting  the  values  of 
A,  A'  and  M  in  the  second  term  of  (14)  we  have  : 


0  = 

V 

and  reducing* 


c  =  (A+A>  -  (II1      ')'-Oy-g')'\  !± 


—  ---  -;  and  g'=  -  7,  and  by  substitution  in  (10) 

8-f-S  S-\-S 


1    *     V\      A+x^)^ fl     ^o^ ii^LJ  j  I 


s-4-s' 
*  Neglecting  the   common   factors  —s—  an(i   '»  and  tlie  denominator,  the 

second  term  becomes, 


2H2—  2g—  2H/2—  2<7/2—  II2—  2HIT— 


2 

_  H2—  2Hir-fH/2—  g*+2(M'—  gf-  _   II— 


"7~     2  2 

and  restoring  the  factors  —    -  and  I,  and  the  denominator,  we  obtain  for 
mula  (1C). 


15 


Reducing  :* 


making  I  =  100,  dividing  by  27,  observing  that  (x—y)*  —  (y—rf  — 
(y~#)2,  and  that  t,    =  a,  we  obtain  : 


y  2  6 

This  is  the  general  formula  when  the  opposite  side  slopes  and  end 
road-bed  widths  are  both  different. 

"When  the  road-bed  widths  are  the  same,  or  b  ~  b'  =  0,  the  last 
term  vanishes,  and  the  formula  becomes  : 


V     2  6 

This  is  the  general  formula  for  all  slopes  and  bases  where  the  base 
is  constant  between  the  two  end  sections. 
When  b  =  l>  =  o,  a  —  o,  and 

H^-^^r-- w 

This  is  the  general  formula  for  the  frustum  of  a  pyramid,f  such  as 
may  be  the  solid  between  two  sections  of  side  hill  excavation. 

The  correction  in  terms  of  equivalent  level  heights  h  and  li'  may 
be  found  directly  from  (16)  as  follows  : 

When  b'  =  b}  the  expression  (g—g'Y  vanishes  and  (1C)  becomes  : 

""  In  squaring  the  binomial  of  radicals  the  f  actors  /_±_  becomes  (i/__l_) 

V   s-}-8'  \r    «+V/ 

in  the  first  term,  |/_?_  ></_*_  in  the  second,  and  L|/_?Lj    in  the  third,  or 

'      6'-(-6/   '      6'-|-6''  *  '      8-^-s'' 

2  8-4-8' 

in  each  —---7.  thus  cancelling  the  factor  —— .  except  in  the  last   term   of  the 

8-\-S  2 

numerator. 

f  Formula  (10)  before  given  for  the  frustum  of  a  pyramid  may  be  traus- 

A      I       A  _|_  A/\A/~       O  A       I     O  A  '     I     O 

formed     into     formula     (19)  ;     for        ~r  *  ~r  V ""   ~r  ^ "J"^ 


3  A-f  3  Ar— A—  A'+2  -y/  A  A'_3(  A+ A')_A— 2  ^/  A  A' + A'_A+ A'_ 
G  0  6~  2~~ 

77^- When  A'=0  in  formula  (19)  it  becomes  C=(^ — —- —  )  —^ 

—  (-A — ~7~' )  ~%Y==~]  ^  ~27~'  w^^  ^s  t^ie  f°rmula  for  ^ie  solidity  of  a  pyramid,  as 

it  should  le. 


10 


but  (H-HT 

and  substituting,  making  I  —  100,  and  dividing  by  27, 


2  0  2V  27" 

As  the  plus  correction  for  calculation  by  middle  area  was  found  to 
be  one  half  of  the  minus  correction  for  averaging  end  areas,  by 
making  the  requisite  changes  in  (20)  : 


but  when  b'  —  b,  from  formula  (12),  we  obtain 


and  by  substitution  : 


This  formula  is  for  use  when  the  equivalent  level  heights  have  been 
obtained. 

APPLICATION   OF   THE    PRISMOIDAL  FORMULA. 

The  prismoidal  formula  in  its  ordinary  form  is  applicable  to  a 
variety  of  solids,  regular  and  irregular,  but  requires  that  the  actual 
middle  section  shall  be  previously  determined  and  its  area  known. 

In  a  modified  form  it  can  be  applied  practically  by  means  of 
tables  ;  such  applications,  however,  always  involving  a  value  of  the 

*  By  substituting  the  values  of  H,  H',  g  and  g'  in  formula  (12)  it  becomes  : 
M  =  V   — 

e 

making  b'=b,  and  squaring  : 


M  = 


4 
b 


,7(+;,u,H;t 

V    8  /       V   «    /^X     2 


4  \   8  /      A"  8  7  '  \    8   /     8 

This  also  results  directly  from  formula  (7)  by  taking  the  area  of  a  second 
section  for  a  height  of  h' ,  and  averaging  like  parts  for  M. 


middle  area  which  can  be  deduced  directly  from  the  end  areas  with 
out  necessitating  a  previous  knowledge  of  the  parts  of  either  the 
middle  or  the  end  sections. 

But  in  all  of  its  modifications,  as  well  as  in  its  ordinary  form,  the 
prismoidal  formula  invariably  involves  the  area  of  the  actual  middle 
section  of  the  solid  to  which  it  is  applied,  and,  as  in  "  Roots  and 
Squares"  and  "  Equivalent  level  heights,''  both  methods  involve  a 
value  of  the  area  of  this  middle  section  (carried  to  intersection  of 
side  slopes  when  in  thorough-cut)  which  can  be  proved  identical 
with  that  of  the  frustum  of  a  pyramid,  the  theoretical  application  of 
these  methods  is  limited  to  solids  with  end  sections  sensibly  similar, 
or  which  can  DC  rendered  so  by  being  carried  to  the  intersection  of 
the  side  slopes. 

As  the  above  has  been  ignored  by  other  writers  on  this  subject,  its 
mathematical  proof  will  be  given. 

The  contents  of  a  frustum  may  be  expressed  either  by  the  pris 
moidal  or  the  frustum  formula,  therefore  in  the  case  of  a  frustum  : 

A+A'+4M  A+A+VAA' 

•  -  —7.  —    ~  X  •  —  ~~       —  o  —      —  X  & 
u  o 

A  I  A  '  I  2  \  /  \  \' 
whence  A+A'-f  4M  =  2A+2A'+2VAA',  and  M  =  -        -~ 


_ 
A          2 

The  formula  of  Roots  and  Squares  where  A  and  A'  represent  the 
end  sections*  is  (Formula  19)  : 

/A+A' 

~ 


and  the  prismoidal  formula  for  the  same  solid  is  : 
n  _  /A+A'+4M\100 

=   -  ~~  ~ 


A+A'+4M    A+A' 
hence-    ^±  -±- 

clearing  fractions,  A+A'+4M  =  3A+3A'-(v/A- 

2A+2A'-A+2VAA7-A' 


_ 


_  / 
V 


In  two  end  sections  with  surface  level  transversely  and  side  slopes 
constant,  if  H  an-1  H'  represent  the  heights  from  intersection  of  side 
slopes  to  surface  and  s  the  ratio  of  the  side  slopes  to  1,  the  areas  of 

*  In  tins  article,  whether  the  end  sections  are  carried  to  intersection  of  side 
slopes  or  not,  their  areas  are  expressed  by  A  and  A'. 


18 

the  end  sections  to  intersection  are  li's  =  A,  and  II'2s  =  A',  and  for 
the  area  of  the  middle  section,  by  averaging  like  parts  : 
/H-fHV     _ 

H  s  r  * 


which  is  the  same  value  of  M  as  that  before  obtained.     Substituting 
this  in  the  prismoidal  formula  : 


<z. __,  and  reducing, 
_ lOG^A+A'-fVAA7     100 

6          ~~x~27~~       3       x~27~ 

which  is  the  formula  for  the  frustum  of  a  pyramid,  and  shows  that 
this  value  of  M  introduced  into  the  prismoidal  formula  limits  its 
application  to  such  solids  only  as  arc  frustums  of  pyramids.  This 
will  be  illustrated  further  from  Example  5,  page  3G,  in  which  when 
carried  to  the  intersection  of  the  side  slopes  produced,  the  end  sec 
tions  are  similar. 

.  Thus  carried  to  intersection,  the  end  areas  and  the  actual  middle 
area  are  respectively  349,  2951,  and  1333,  as  given  page  3(j. 
By  Roots  and  Squares 

=  1332 


By  equivalent  level  heights 

II  =  y  -  =  y  349x  |=  15.25 


II'  -V  —=V  2951x1  =  44.35 

8 


By  substituting  this  value  of  M  in  the  prismoidal  formula  : 
C  =3JO+ 


For   calculation   by  equivalent  level  heights  as  table  15  has  a 
base  of  14  feet,  and  the  above  heights  are  taken  to  intersection  of 

side  slopes,  (-       -)  x!4x-k-^r  must  be  deducted  from  contents 
\      ~      /  ^7 

taken  from  tables. 


19 

By  Rule  4, 


^  29.8  table  15..  6,47* 


& 
15.25~44.35  =  29.1  table  17.  .+  392 

6,871 

Deduct  29.8x14  X^  =  417.2  table  4.  .  .—1,545 


5,336  cyds. 
By  mean  proportional  or  frustum  formula  : 


1  00 
By  deducting  tlie  grade  prism  32.7  X  -^y  =  121  cyds.,  practically 

the  same  result  as  that  given  on  page  36  is  obtained. 

Another  case  in  which  the  area  of  the  actual  middle  section  can 
be  deduced  from  the  end  areas  directly,  is  when  each  of  the  latter 
can  be  expressed  by  two  surface  dimensions,  one  of  which  is  the 
same  for  both  end  sections,  as  in  solids  whose  end  sections  are 
parallelograms  or  triangles  with  the  same  base  and  different  heights, 
or  vice  versa.  Thus  if  Hi  =  A  and  lhr  =  A'  represent  the  end  areas 
of  a  solid  of  which  the  end  sections  are  triangles  with  the  same 
base  and  different  heights,  as  may  be  the  case  in  side  hill  cutting 
where  the  transverse  surface  slope  increases  regularly  between  the 
end  sections,  by  averaging  like  parts  the  middle  area  is 

v   i(lt+n'\  m+w  A+A/ 
*(-*-)=  "    — 

And  as  the  prismoidal  formula  is  applicable  here,  by  substituting 
this  value  of  M  : 


~s~        ~XW'    -—'W 

which  is  the  average  area  formula,  in  this  case  giving  the  prismoidal 
contents.  As  an  example,  suppose  the  triangular  end  sections  of 
the  solid  to  have  a  base  of  20  feet  and  heights  of  10  and  40  feet 
respectively.  Then  A  —  10  x  10  =  100  ;  A'  =  10  x  40  =  400  ;  and 


£ 

By  the  prismoidal  formula  : 

n       100  +  400  -f  4  x  250     100 

C=-  —-  -x-  =  250  table  4...  926  cds. 


20 


Calculated  by  Roots  and  Squares  M  =  \  __  935 

\  2  / 

and  this  substituted  in  the  prismoidal  formula  gives 

100 


C  = 

U  /v  l 

^ 

Here  the  average  area  formula  gives  the  prismoidal  contents,  and 
the  prismoidal  formula  applied  by  its  modification  of  Roots  and 
Squares  gives  a  very  rough  approximation.  The  same  inaccuracy  is 
of  course  involved  in  the  method  by  equivalent  level  heights,  what 
ever  may  be  the  shape  of  the  equivalent  and  similar  end  sections  of 
which  the  level  heights  are  obtained.  For  instance,  if  the  side  hill 
work  is  excavated  at  rock  slope,  the  level  heights,  if  carried  to 
vertex,  may  be  taken  for  sections  with  any  other  side  slopes,  as  1  to 
1,  or  1J-  to  1. 


At  1  to  1  carried  to  vertex  H  =  |/^=  10  ;  IT  =  \/~~  = 

20,  and  to  calculate  by  table  12,  with  side  slopes  1x1  and  base  18 
feet: 


—  =  15  table  12  ..............  1833 

2 

10-20  =  10  table  14  ...............  +31 

Deduct  15xl8x-~  =  270  table  4  ............  -1000 

864  cyds. 

at  1£  to  1  carried  to  vertex  II  =  V^00x"f  =  8.16  ;  H'  =  -\AOOxf 
=  16.33,  and  to  calculate  by  table  15,  with  side  slopes  1£  to  1,  and 
base  14  feet. 

8-1C+16'33=  13.845  table  15  .......  1468 

« 

8.16—16.33  =      8.17  table  17  .......  +31 

Deduct    12.245xl4x^=  171.4  table  4  .......  -635 

/v  • 

864  cyds. 

The  two  last  examples  show  the  same  error  of  62  cyds.  obtained  by 
Equivalent  level  heights,  as  before  by  Roots  and  Squares. 
I?y  mean  proportionals  or  frustum  formula  : 


21 

By  Rule  2, 


926 


10~20      =    18  table5..  .  62 


864  cyds. 

If  the  above  sections  were  similar,  as  for  instance  with  dimensions 
10  x  10  and  20  x  20,  the  first  method  by  average  areas  would  give 
too  much  by  62  cyds,  whilst  by  the  others  the  true  prismoidal  con 
tents  would  be  obtained. 

If  both  the  heights  and  bases  are  different  and  the  sections  are 

A-f-A' 

not  similar,  the  middle  area  will  be  less  than  -       -  and  greater 

tit 

than  I V  A-fv  A  \  ^  an^  canno^  j^  obtained  directly  from  the  end 

\  JO  r 

areas.  In  such  cases,  the  exact  contents  can  be  determined  by  the 
prismoidal  formula  only  by  first  obtaining  the  dimensions  of  the 
actual  middle  section  and  calculating  its  area. 

Practically  in  railroad  earthwork  it  is  only  when  the  transverse 
surface  lines  of  the  end  sections  are  very  dissimilar  and  the  areas 
differ  greatly  in  size  that  the  resulting  errors  become  important,  and 
as  at  such  points  the  cross  sections  are  usually  taken  nearer 
together,  it  is  very  rarely  the  case  that  the  methods  of  Eoots  and 
Squares  and  Equivalent  level  heights  fail  of  practical  correctness. 
In  cases  of  doubt,  however,  especially  when  the  surface  is  warped 
between  the  end  sections,  it  is  safer  and  better  to  obtain  the  area  of 
the  actual  middle  section  before  calculating  the  contents. 


CORRECTION    OF    CONTENTS    FOR    CURVATURE. 

The  following  article  was  suggested  by  that  given  in  Henck?s 
"  Field  Book/'  page  110. 

In  excavation  on  curves,  although  the  cross  sections  are  actually 
staked  out  in  the  direction  of  the  radii  at  the  extremities  of  the 
chords,  the  calculation  of  contents  is  made  as  if  these  cross  sections 
were  perpendicular  to  the  chords.  In  some  cases,  especially  where 
the  transverse  surface  slope  is  considerable,  this  is  the  occasion  of  a 
sensible  error  requiring  a  corresponding  correction,  the  amount  of 
which  is  determined  as  follows  : 

>^  OP  THE"^ 


Fig.  6. 


Suppose  A,  B,  and  C  to  be  three  consecutive  100  feet  stations 
on  a  curve  of  radius  OB ;  and  BF  and  BII  the  side  distances  at 
station  B. 

The  calculation  of  contents  between  A  and  B,  and  B  and  C 
made  as  if  the  cross  sections  at  these  points  were  on  the  lines  KjLj. 
and  KL,  and  K'L'  and  K3L2,  or  perpendicular  to  the  chords  AB 
and  BC,  requires  at  each  station  a  correction  similar  to  that  at  B, 
which  will  now  be  considered.  It  is  evident  that  the  correction  is 
the  difference  between  the  masses  KBK'  and  L'BL,  on  opposite 
sides  of  the  centre  line,  and  between  the  two  vertical  planes  KL  and 
K'L' ;  these  masses  having  for  their  cross  sections  respectively  the 
half-breadths  BF  and  BH.  The  angle  KBK'  being  very  small,  the 
arcs  KFK'  and  L'HL  will  be  considered  as  straight  lines  ;  and,  as 
the  angle  KBF  =  L'BII  =  $  KBK'  =  TBA  =  D,  the  deflection 
angle  of  the  curve,  the  distance  KF  =  BF  x  sin  D  ;  or,  generally 
for  small  angles,  any  horizontal  line  as  KK'  or  L'L  measured  per 
pendicularly  to  the  radius  OB,  and  terminated  by  the  planes  KL 
and  K'L',  is  practically  equal  to  BF  or  BH  (the  corresponding 
horizontal  distance  from  the  centre  line)  multiplied  by  2  sin  D. 
Consequently,  the  masses  KBK'  and  L'BL  being  considered  as  trun 
cated  prisms  with  the  areas  of  the  half-breadths  BF  and  BH  as 
bases,  their  heights  at  any  given  points  are  equal  to  the  horizontal 
distances  of  these  points  from  the  centre  line,  multiplied  into  twice 
the  sine  of  the  deflection  angle. 


Fig.  7. 


Conditions. — Sin 
gle  width  road-bed 
and  opposite  side 
slopes  the  same. 
Transverse  surface 
slopes  regular, 


Let  FBHT  represent  the  cross  section  at  B  (Fig.  C). 
To  simplify  calculations,  the  equal  prisms  MPT  and  PTX  are 
added. 


The  area  FBT  =  (BP+PT)  ±  -  =  (c+~r-,  and  the  heights 

/y  y        '/is /  lv 

of  the  prism  corresponding  are  =  d  x  2  sin  D  at  F,  and  =  0  at  B 
and  T.     Its  contents  therefore  =  /  c~i~7"  feX  (  ~  ^~q~    ~  )•   Similarly 


.        TTT>rn 

the  contents  of  prism  HBT  := 


2sinD\ 
?,  —    ~)  an(^- 


correction  required,    which    is  the    difference   of   their  volumes, 
I    dz     2  sin  D  b  \cr     2  sin  D 


and  if  Q  represents  the  required  correction  in  cubic  yards, 


But,  from  formula  (1),  |c-[-~)(  -     -J  =  A+«,  the  area  carried 
to  intersection  of  side  slopes  ;  also  sin  D  =      ,  and  as  E  —  -g-  ,  in 


24 

C° 
which  C°  represents  the  degree  of  curve,  2  sin  D  =  50  x  2  x  ^r 

o  i «[ 

0° 
"57.3 

Therefoie, 

0  =  (A+«)  C°x  — ^^— (23) 

57.3x3x27    • 

In  side  hill  work,  as'  shown  by  Mr.  Ilenck,  the  general  formula 

wli  ,-,,-,        ,100 
lor  the  correction  in  cubic  feet  is  Q  =  —  (d-\-o— w)-^,  in  which 

*i  ol\ 

w  represents  the  width  of  excavation  at  the  road-bed.     But  as  — - 

=  A,  the  area  of  earthwork,  in  this  case  the  correction  in  cubic 
yards  is 


57.3x3x27 

Values  of  the  last  factor  in  formulae  (23)  and  (24)  are  given  in 
Table  18. 

In  excavation  the  correction  for  curvature  as  obtained  by  for 
mulas  (23)  and  (24)  is  to  be  added  when  the  curve  is  convex,  and 
subtracted  when  it  is  concave  toward  the  higher  ground,  and  in  em 
bankment  these  conditions  are  reversed.  It  is  supposed  to  be 
applied  at  the  middle  one  of  three  cross  sections  at  intervals  of  100 
feet,  and  all  on  the  same  curve. 

If  the  distance  to  either  of  the  cross  sections  next  the  one  under 
consideration  differs  from  100  feet,  the  correction  found  as  above  is 
to  be  multiplied  by  the  half  sum  of  the  two  distances  and  divided  by 
100. 

At  points  of  curve  or  tangent  one  of  these  distances  of  course 
becomes  nothing. 

Whether  the  side  slopes,  or  the  widths  from  the  centre  line  to 
the  edge  of  the  road-bed,  are  different  or  not,  if  the  transverse  sur 
face  lines  are  broken,  the  cross  sections  should  be  drawn  to  scale, 
the  two  half -breadths  divided  into  triangles,  and  the  horizontal  dis 
tances  from  the  centre  line  to  the  corners  of  each  subdividing 
triangle  measured  on  the  drawing.  The  sum  of  the  three  distances 

2  sin  I) 
for  each  triangle  multiplied  by  its  area  and  by  — - —  will  give  the 

contents  in  cubic  feet  of  the  prism  corresponding.  It  is  not  mate 
rial  how  the  sides  of  the  subdividing  triangles  are  drawn,  provided 
that  the  whole  of  each  triangle  is  on  the  same  side  of  the  centre  line. 
The  difference  of  the  masses  whose  cross  sections  are  the  half- 


25 

breadths  FB  and  BH  (Fig.  G),  and  which  lie  on  opposite  sides  of  the 
centre  line  between  the  vertical  planes  KL  and  K'L',  the  base  plane 
and  the  planes  of  the  side  slopes,  is  in  all  cases  the  correction 
required. 

With  double-width  track  or  opposite  side  slopes  different,  if  the 
surface  is  regular  from  the  centre  to  the  slope  stakes,  from  formula 

(3),  the  areas  of  the  triangles  of  one  half  -breadth  are  -  x/'i  and  —  , 

and  of  the  other  -rX/^o  and  — 

The  heights  of  the  prisms  corresponding  to  these  areas  are 

2  sin  D  ;  (d+O+O)  |  sin  D  .    /  ^'_|_|+o)  f  sin  D  ;    and 
(J'-f-O-fO)  |  sin  D,  and  their  contents 

sin  D          shl  D      x"     d/+     sin 


and  (-|-)f  sin  D  ;  but  as  f  55—.  =  C°x  0.000215,   the  correction 
in  cubic  yards  becomes 


d~d')  \  C°x  0.000215  ..........  (25) 


PART  II. 


PLAIN  INSTRUCTIONS 

FOR   OBTAINING  THE   PRISMOIDAL  CONTEXTS   OF   EARTHWORK,  WITH 
PRACTICAL   RULES   AND   EXAMPLES   SHOWING   THE   USES   OF  THE 
ACCOMPANYING    TABLES   IN   SIMPLIFYING   COMPU 
TATIONS   BY  THE   FORMULAE   OF   PART   I. 

THE  following  Rules  for  computation  of  Cubic  Contents  are  based 
on  the  condition  that  the  transverse  surface  lines  of  the  end  sections 
shall  be  sensibly  similar ;  but  it  will  be  observed  that  1,  2,  and  3 
together  coverall  cases  to  which  the  method  of  "  Roots  and  Squares,''' 
or  of  "  Equivalent  level  heights,"  can  be  correctly  applied,  and  that 
the  practical  limit  of  their  application  may  be  indefinitely  extended 
by  increasing  the  proximity  of  the  cross  sections  in  rough  ground. 

To  find  the  prisvtioidal  contents  of  thorough-cut  or  Jill  when  road-bed 

width  and  side  slopes  are  constant  between  end  sections. 
Given  :  areas,  side  slopes,  and  base  (A  and  A',  s  and  s',  and  b). 

RULE  1. — (FORMULA  18). 
Enter  table  2  with  the  given  road-bed  width  (#),  and  the  half 

(X-L-,S''\ 
^— J,  and  take  out  the  corre 
sponding  area  =  a.     Add  this  to  each  of  the  given  end  areas  and  the 
square  roots  of  the  resulting  quantities  (<\/A-|-ft  and  \/A'-{-aj  from 
table  3  are  N  and  N',  the  correction  numbers. 

Enter  table  4  with  the  average  of  the  end  areas  (    "^      )>  an(l 

table  5  with  the  difference  of  the  correction  numbers  (N~N'),  and 
take  out  the  corresponding  quantities.  The  difference  of  the  quan 
tities  taken  from  tables  4  and  5  is  the  contents  in  cubic  yards  for  a 
length  of  100  feet. 

For  a  different  length  multiply  by  the  length  iu  feet  and  divide 
by  100. 

Example.— Given  A  -  974  ;  A'  =  87  ;  ,9  =  i  ;  s'  =  £  ;  I  =  20. 


27 


s-4-s' 
From  table  2  when  b  =  20  and  -77™  =  f>  ^ne  area  °*  tne 

triangle  («)  =  160 


<V/A-f-«  =  V974  +  160  =  1134  table  3 33.7  =  N 

^/A^a  =  A/87  +  160  =    247  table3 15.7  =  X' 

A+A'      974+87       _  K  ,  , , 

— Z_ —  = _I —  —  o30. 5  table  4 196o 

2  2 

N~N'  i=  33.7~15.7  =  18.0  table  5. .       . .  —200 


Contents  for  100  feet  ..........  1765  cyds. 

For  a  different  length  as  80  feet,  1765  x  0.8  =  1412  cyds. 
XOTE.  —  If  the  square  roots  of  the  areas  to  the  intersection  of  the 
side  slopes  are  obtained  and  recorded  when  the  areas  are  calculated, 
as  will  ordinarily  be  found  more  convenient,  the  data  are  A  and  A' 
and  N  and  N;,  and  only  the  two  last  steps  of  Rule  1  are  necessary. 

To  find  the  prismoidal  contents  of  side  hill  work,  pyramids,  and  any 
solid  with  similar  end  sections. 

Given  :  end  areas  (A  and  A'). 

RULE  2  (FORMULA  19). 

Take  the  square  roots  of  the  end  areas  (A/  A  and  A/  A7)  from 
table  3  =  n  and  ri. 

Enter  table  4  with  the  average  of  the  end  areas  (  -    —  V  and 

\     2     / 

table  5  with  the  difference  of  the  correction  numbers  (n~ri),  and 
take  out  the  corresponding  quantities.  The  difference  between  the 
quantities  taken  from  tables  4  and  5  is  the  contents  in  cubic  yards 
for  100  feet. 

For  a  different  length  multiply  by  the  length  in  feet  and  divide 
by  100. 

Example.  —  Given  end  areas  A  =  41  and  A'  =  185. 

A/A  =  41  table  3  =  6.4  =  n;  A/  A7  =  183  table  3  =  13.6  =  n'. 

_  £+185  =  113teble4  .......  418.5 

/  & 

ri  =  6.4—13.6  =  7.2  table  5  .......   32.0 


Contents  for  100  feet  ...........  386.5  cyds. 


For  a  different  length,  as  25  feet,  —  -^-—  =  96.6  cyds. 

Example.  —  Pyramid.     Given  end  areas  A  =  104  and  A'  =  0. 
A/A  =  104  table  3  =  10.2  =  n  ;  A/A7  =  0  =  n. 


28 

A+A'       1044-0 

_Z —  _  — IL_  —  02  table  4 192.G 

n~ri  =  10.2-0  =  10.2  table  5 -64.2 

Contents  for  100  feet 128. 4  cyds. 

For  a  different  length,  as  GO  feet,  128.4x0,6  =  77  cyds. 

KOTE. — Examples  under  Rule  1  can  be  readily  tested  by  Rule  2, 
the  difference  in  the  working  being  that  the  •grade  prism  is  first 
included  and  then  deducted.  For  instance,  in  the  example  given 
under  Rule  1,  the  end  areas  to  intersection  of  side  slopes  are  1134 
and  247,  and  the  square  roots  corresponding  33.7  and  1G.7 — then  : 
.1134^-247  =  G95> 

2 
33.7-15.7  =  18.0  table  5 . .  . .  -200 


Contents  to  intersection  of  side  slopes . .  .2358 
Less  grade  prism  160  table  4 —593 

Contents  of  earth  work  for  100  feet..  1765  cyds. 

To  find  the  prismoidal  contents  of  thorough-cut  or  fill  when  the  end 
road-bed  widths  are  different. 

Given  :  end  areas,  side  slopes,  and  end  road-bed  widths  (A  and  A'; 
s  and  s' ;  1)  and  V). 

RULE  3  (FORMULA  17). 

g  I  <•' 
Enter  table  2  with  •—£—  and  Z>,  V  and  l~l'  respectively,  and 

/v 

take  out  the  corresponding  areas  a,  a'  and  a".  From  table  3  take 
out  the  square  roots  of  the  end  areas  to  intersection  \/A+a  =  N", 
and  \/A'-\-a'  =  X'. 

Enter  table  4  with  —    - — (-— ,  and  table  5  with  N"~N',  and  the 
/&         o 

difference  between  the  corresponding  quantities  taken  from  tables  4 
and  5  is  the  contents  in  cubic  yards  for  100  feet.  For  a  different 
length  multiply  by  the  length  in  feet  and  divide  by  100. 

Example.— Given  I  =  16  ;  V  =  40  ;  s  =  J  ;  5'  =  | - ;  A  =  1565  ; 
A'  =  253. 

Here  a  =  128  ;  a'  =  800  ;   a"  =  288  ;  N  =  41.1  and  N'  =  32,4. 

A+A     a"     1565+253,288     QKW ,  v, 

-^ — HTT^ ^- +y-  =  9o7table4 3o44.4 

X~:\T/  =  41.1-32.4  =  8.7  tablc  5 -46.7 

Contents  for  100  feet 3497.7 

Q  \  Q*V  *y 
For  a  different  length,  as  50  feet — 5—  =  l^49  cyds. 


29 

The  example  under  Eule  3  is  of  a  case  where  averaging  the  end 
areas  gives  less  than  the  prismoidal  contents.  It  may  be  tested  by 
Formula  8,  page  12,  as  also  Rules  1  and  2  by  Formulae  9  and  10. 

To  find  the  prismoidal  contents  when  the  ground  is  level  transversely, 
or  where  the  heights  of  equivalent  level  sections  have  been  obtained. 

Given  :  level  heights,  base  and  half -sum  of  ratios  of  side  slopes 
and  h' ;  I  and  ^±l'Y 

RULE  4  (FORMULA  21). 
Enter  the  table  of  level  cuttings  for  the  proper  base  and  side 

slopes  with  the  half -sum  of  the  end  heights  (  -     -),  and  the  table 

\    *    / 

of  special  plus  corrections  for  the  same  side  slopes  with  the  diffe 
rence  of  the  end  heights  (h~hr),  and  take  out  the  corresponding 
quantities.  The  sum  of  these  quantities  is  the  contents  for  100  feet. 
For  a  different  length,  multiply  by  the  length  in  feet  and  divide 
by  100. 

Example.— Given  I  =  14  ;  h  =  8.6  ;  ///  =  36.8  ;  ^ti  =  H. 

=  m  table  15..  ..4040 

x>  £ 

h~h'  =  8.G~3G.8  =  28.2  table  17 +368 

Contents  for  100  feet 4408  cyds. 

For  a  different  length,  as  85  feet,  4408  x  0.85  =  3747  cyds. 

To  find  the  Correction  for  Curvature  in  single  width  thorough-cut 
when  the  transverse  surface  slope  is  regular. 

Given  :  area  to  intersection  of  side  slopes,  degree  of  curve,  and 
difference  of  side  distances  (A-\-a,  C°,  and  d~d'). 

RULE  5  (FORMULA  23). 

Enter  table  18  with  d~d'  and  take  out  the  corresponding  factor  : 
multiply  this  into  the  product  of  A+«  by  C°,  and  the  result  is  Q 
the  correction  in  cubic  yards,  to  be  applied  at  the  middle  one  of 
three  stations,  all  on  the  same  curve  and  100  feet  apart.  If  the  dis 
tance  to  either  of  the  other  two  stations  from  the  middle  one  differs 
from  100  feet,  multiply  by  the  half -sum  of  the  two  distances  and 
divide  by  100. 


30 

This  correction  is  to  be  added  or  subtracted  accordingly  as  the 
curve  is  convex  or  concave,  toward  the  higher  ground. 

Example,—  Given  c  =  28  ;  7^  =  40  ;  h2  =  16  ;  d  =  74  ;  rf'  =  38  ; 
6  =  28  ;  E  =  1400  ;  or  A+«  =  2090  ;  C°  =  4°.09  ;  d~d'  =  30. 

36  table  18  =  0.00776, 
ami  2090x4.09x0.00776  =  66.3  cyds. 

If  the  distances  to  the  two  adjacent  stations  are  50  and  40  feet 


respectively,  the  correction  required  is  —  •~X^6.3  =  GG.3xO.-l  5 

=  29.8  cyds. 

To  find  the  correction  for  curvature  in  side-hill  work  when  the  trans 
verse  surface  slope  is  regular. 

(liven  :  area  ;  degree  of  curve  ;  side  distance  ;  road-bed  width  ; 
and  width  of  excavation  at  road-bed  (A  :  C°  ;  d;  b  ;  w). 

RULE  6  (FORMULA  24). 

Enter  table  18  with  d-\-l)  —  io  and  take  out  the  corresponding 
factor  :  multiply  this  by  the  product  of  A  by  C°,  and  the  result  is 
Q  the  correction  in  cubic  yards,  to  be  applied  in  all  respects  as  in 
Rule  5. 

Example.—  Given  w  —  17  ;    b  —  30  ;    d  -  51  ;    7/t  =  24  ;    1!  = 
•1600  ;  or  A  =  204  ;  C°  =  3°.5S  ;  d+l-w  =  64. 

G4  table  18  =  0.01379, 
and  204x3.58x0.01379  =  10.1  cyds. 

If  both  intervals  are  50  feet,  the  correction  required  is  ~^~ 

X  10.1  =  10.1  X  0.5  =  5  cyds. 

For  correction  for  curvature  when  the  transverse  surface  slope  is 
broken,  or  for  double-width  thorough-cut,  sec  page  24. 

Rules  5  and  6  apply  to  excavation  only.  For  embankment  the 
correction  is  to  be  added  or  subtracted  accordingly  as  the  curve  is 
concave  or  convex  toward  the  higher  ground. 


31 


MISCELLANEOUS  EXAMPLES. 
EXAMPLE  1. 


(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

(?) 

(8) 

(3) 

(10) 

ss  o 

02  .2 

«§ 

fig 

End 

Areas. 

Average 
Areas. 

Corr'n 

Areas. 

Corr'n 
sq.  roots 

Diff. 
sq. 
roots 

Average 
Contents. 
cu.  yds. 

Corr'n 
Contents, 
cu.  yds. 

Prismoidal 
Contents, 
cu.  yds. 

| 

0 

0.0 

0.0 

0.( 

80 

30.0 

7.7 

88.9 

29.3 

59.6 

fl 

GO.O 

j   60.0  M    7.71 
U60.0J   J12.6  f 

60 

96.2 

2.6 

213.8 

2,5 

2113 

1 

132.5 

232.5 

15.2 

100 

190.9] 

3.5 

707.0 

7.6       699.4 

3 

249.2 

349.2 

18.: 

100 

280.9 

1.6 

1040.3 

1.6 

1038.7 

5 

312.7 

412.7 

203 

100 

466.6 

6.5 

1728.1 

26.1 

1702.0 

w 

< 

G20.5 

720.5 

26.8 

i 

100 

682,6 

2.3 

2528.1 

3.3 

2524.8 

9 

744.8 

844.8 

29.1 

100 

864.9 

3.8 

3203.3 

8.9 

3194.4 

11 

985.0 

1085.0 

32.9 

100 

893.3 

2.9 

3308.5 

5.2 

3303.3 

13 

801.5 

901.5 

30.0 

100 

608.7 

I 

7.3 

2254.4 

32.9 

2221.5  ; 

15 

416.0 

516.0      22.7 

. 

100 

287.8 

6.6 

1065.9 

26.9 

1039.0 

17 

159.5 

259.5 

16.1 

1 

40 

129.7 

2,0 

192.1 

1.0 

191.1 

rt 

100.0 

1  200.0  1 
1  100.0  f 

m.i) 
Uo.0  f 

50 

50 

10.0 

92.6 

30.8 

61.8 

0 

0.0 

0.0 

0.0 

1 

16423.0 

-176.1 

=16246.9 

1 

Example  1,  as  above,  is  of  the  railroad  cut  given  in  Morris's 
"Earthworks,"*  pp.  47-54,  with  contents  computed  by  Rules 
1,  2,  and  4,  and  the  auxiliary  tables  of  the  present  work.  As 
here  used,  the  areas  are  supposed  to  belong  to  sections  which,  when 
carried  to  the  intersection  of  the  side  slopes  in  thorough-cut,  are  ren 
dered  sensibly  similar,  and  the  examples  as  here  given  are  intended 

*  "Easy  Rules  for  the  Measurement  of  Earthworks  by  means  of  the  Pris 
moidal  Formula.  By  Ell  wood  Morris,  C.E."  Philadelphia  :  1872. 


32 

to  show  only  the  comparative  facility  of  arriving  at  the  prismoidal 
contents  by  Mr,  Morris's  methods  and  those  of  the  preceding  rules 
when  the  above  condition  of  similarity  is  fulfilled,  and  not  to 
endorse  the  application  of  the  method  of  "  Roots  and  Squares  "  (or  of 
the  rules  of  this  work)  in  cases  where  the  hypothetical  middle  area 
materially  differs  from  the  actual  one.* 

Except  by  trial  with  the  actual  middle  section  and  the  prismoidal 
formula,  it  seems  almost  impossible  in  cases  of  dissimilar  end  sections 
to  know  when  the  application  of  the  method  of  Roots  and  Squares,  or 
of  the  preceding  rules,  begins  to  fail  of  practical  correctness,  but  it 
may  safely  be  assumed  that  if  the  ground  is  properly  and  sufficiently 
cross-sectioned,  the  results  obtained  by  them  will  be  practically  the 
prismoidal  contents. 

The  above  tabulated  example  shows  all  the  steps  necessary  .in 
(hiding  the  prismoidal  contents  in  cubic  yards  when  the  areas  are 
given.  Columns  (1),  (2),  and  (3)  being  written  out,  (4)  is  derived 
directly  from  (3)  by  averaging  ;  (5)  from  (3)  by  adding  area  of  grade 
triangle  in  thorough-cut ;  (G)  from  (5)  by  table  3  ;  (7)  from  (G)  by 
subtraction  ;  (8)  from  (4)  by  table  4  ;  (9)  from  (7)  by  table  5  ;  and 
(10)  from  (8)  and  (9)  by  subtraction. 

Column  (4)  gives  the  average  end  areas  throughout  the  cut, 
including  the  terminal  pyramids,  and  the  only  break  in  the  routine 
of  adding  the  area  of  the  grade  triangle  in  column  (5)  is  at  the  point 
where  the  cutting  runs  out  on  the  lower  side.  At  such  points  two 
areas  have  to  be  used,  the  one  of  earthwork  plus  the  grade  triangle, 
for  computation  of  thorough-cut  by  Rule  1,  and  the  other  of  earth 
work  alone,  for  the  calculation  of  the  pyramid  or  side-hill  work 
into  which  the  thorough-cut  changes,  and  of  which  the  computation 
of  contents  falls  under  Rule  2. 

Column  (8)  gives  the  contents  between  each  two  stations  roughed 
out  by  the  common  method  of  "  average  areas,"  column  (9)  the  cor 
responding  error,  and  column  (10)  the  prismoidal  contents,  all  in 
cubic  yards. 

It  is  not  strictly  necessary  to  write  out  all  of  the  columns  given 
above,  but  errors  are  so  much  more  readily  detected  when  all  of  the 
steps  are  shown,  that  ordinarily  time  and  labor  will  be  saved  by 
adopting  some  system  of  tabulating  similar  to  the  above,  both  as 
regards  the  number  of  columns  and  the  arrangement  by  which  the 
figures  ref en-ing  to  each  two  stations  may  be  recorded  on  a  line 
between  them. 

*  See  article  on  the  application  of  the  prismoidal  formula,  page  16. 


33 


The  prismoidal  contents  in  cubic  yards  between  stations  1  and  1 7 
are  given  by  Mr.  Morris  as  15,721,  and  by  the  above  computation  as 
15,723,  whilst  the  contents  of  the  whole  cut  given  by  him  as  16,664 
appear  above  as  16,247.  The  discrepancy  is  in  the  truncated  por 
tions  of  the  cut  outside  of  stations  1  and  17,  which  by  some  over 
sight  he  gives  as  943,  instead  of  524  cubic  yards. 

The  preceding  example  will  now  be  computed  by  equivalent  level 
heights  and  Rule  4.  The  data  of  level  heights  are  supposed  to  be 
obtained  from  Trautwine's  diagrams,  as  when  such  accuracy  is 
required  as  renders  the  calculation  of  areas  necessary,  Rule  1,  2,  or  3 
should  be  used  for  the  computation  of  contents. 

EXAMPLE  2. 


0) 

(2) 

(3) 

(4) 

(5) 

(6) 

(7) 

(8) 

Stations.    Distances. 

Eq.  Level 

Heights, 

Eq.  Level 
Heights. 
Half-sum. 

Eq.  Level 
Heights. 
Difference. 

End 
Heights. 
Contents. 

Corr'n 
Contents, 
cu.  yds. 

Prismoi 
dal 
Contents, 
cu.  yds. 

0 

0.7 

40 

1.6 

1.9 

51 

0 

51 

a 

2.6 

60 

3.9 

2.6 

207 

1 

208 

I 

5.2 

100 

7.0 

3.5 

700 

4 

704 

3 

8.7 

100 

9.5 

1.6 

1038 

1 

1039 

5 

10.3 

100 

13.6 

6.5 

1692 

13 

1705 

7 

16.8 

100 

18.0 

2.3 

2533 

2 

2535 

9 

19.1 

100 

21.0 

3.8 

3189 

5 

3194 

11 

22.9 

100  | 

21.5 

2.9 

3305 

3 

3308 

13 

.20.0 

100  | 

16.4 

7.3 

2211 

16 

2227 

15 

12.7 

100 

9.4 

6.6 

1024 

13 

1037 

17 

6.1 

40 

5.1 

2.0 

190 

0 

190 

a 

4.1 

25 

2.6 

3.1 

54 

1 

55 

0 

1.0 

16194 

-f-59  = 

16253 

34 

Yfitli  equivalent  level  heights  given,  the  above  tabulated  example 
shows  all  the  steps  required  in  finding  the  approximate  prismoidal 
contents  in  cubic  yards.  Columns  (1),  (2),  and  (3)  being  written 
out,  (4)  is  derived  directly  from  (3)  by  averaging,  and  (5)  from  (3) 
by  subtracting.  The  table  of  level  cuttings  for  a  base  of  20  feet  and 
slopes  1  to  1,  from  which  column  (G)  should  be  taken,  is  not  pub 
lished  in  this  volume,  but  its  place  may  readily*be  supplied  by  adding 
1.  to  each  of  the  heights  of  column  (3),  and  taking  70  from  each  of 
the  corresponding  quantities  in  table  12.  Such  remainders  are  the 
amounts  in  column  (G).  Column  (7)  is  derived  from  (5)  by  table 
14,  and  (&)  from  (G)  and  (7)  by  addition. 

In  ordinary  ground  sloping  transversely,  the  area  of  earthwork  of 
the  terminal  pyramid  at  the  point  where  the  centre  height  is 
nothing,  is  about  one-fourth  of  the  area  of  the  section  where. the 
pyramid  begins  ;  and  practically,  as  only  small  quantities  are  con 
cerned,  the  equivalent  level  height  corresponding  may  be  taken  as 
one-fourth  of  that  corresponding  •  to  >tho  area  of  the  base  of  the 
pyramid. 

The  calculation  of  contents  by  equivalent  level  heights  and 
tables  is  well  suited  for  preliminary  or  approximate  estimates,  espe 
cially  if,  as  in  the  present  case,  when  the  sum  of  the  tenths  of  the 
end  heights  is  uneven,  the  average  is  always  taken  as  the  tenth  next 
greater  than  the  actual  half-sum. 

The  variation  between  the  contents  of  the  thorough-cut  from  1  to 
17,  as  given  in  Examples  1  and  2,  is  due  to  the  fact  that  the  equiva 
lent  level  heights  are  carried  out  to  tenths  only.  In  the  present 
case,  at  a  height  of  20  feet  the  increment  is  over  two  cubic  yards  for 
each  0.01  of  a  foot,  and  in  embankment  at  the  same  height  it  is 
still  greater.  As  in  practice  neither  equivalent  level  heights  nor 
those  of  the  tables  of  level  cuttings  are  carried  out  to  hundredths, 
one  cause  of  the  greater  accuracy  of  the  previous  method  by  Rules 
1  and  2  is  evident.  It  may  be  replied  that  errors  as  important  arc 
involved  in  the  field  work,  the  cross  section  stakes  being  set  only 
approximately  ;  but  that  an  element  of  error  should  voluntarily  be 
introduced  into  the  calculations  because  another  such  already 
exists  in  the  data,  is  a  position  that  will  not  be  contended  for 
seriously. 

Example  3. — In  a  cutting  with  road-bed  width  1G  feet,  and  oppo 
site  side  slopes  J  and  f  to  1,  the  given  areas  of  two  consecutive  cross 
sections  with  similar  transverse  surface  lines  and  at  a  distance  apart, 
of  100  feet,  arc  100  and  1000  square  feet  respectively  :  required 
the  prismoidal  contents.  Here  the  area  of  the  grade  triangle  (table  2) 


OJ 

is  102,  and  consequently  the  whole  areas  to  intersection  are  202  and 
1102. 

To  find  the  correction  numbers  N and  JV. 

202  table3 14.2  =  JV 

1102  table  3 33.2  =  N' 

To  find  the  contents  in  cubic  yards. 
100+1000 


=  550  table  4. 


2 
14.2-33.2  =  19.0  table  5. .  ..-223 


Contents  for  100  feet 1814  cyds. 

Test  by  Formula  9. 


-Y/202xll02  =  472  =  mean  area  to  intersection. 


=  490  table  4  ..........................  1815  cyds. 

Example.  4.  —  Given  100  and  1000  square  feet  respectively  as  the 
areas  of  two  similar  cross  sections  100  feet  apart,  irrespective  of 
shape  or  number  of  sides  in  perimeter  :  required  the  prismoidal  con 
tents. 

To  find  the  correction  numbers  n  and  n. 
100  table  3  ......................  10.0  =  n 

1000  table  3  .....................  31.6  =  n' 

To  find  the  contents  in  cubic  yards. 


A 

10.0—  31.  G  =  21.6  table  5  .  .  .—  288 


Contents  for  100  feet 1749  cyds. 

Test  by  Formula  10. 
=  316  =  mean  area. 


/1 00+1000+316X100          -0/100\ 

I          •    r=  4:  i  fi  \  —. — -  I 

V  3  /27  \2lJ 

=  472  table  4 , 1748  cyds. 

Example  5. — At  two  stations  100  feet  apart  with  base  b  =  14  feet, 
and  side  slopes  s  =  1|-  to  1,  given  the  notes  of  the  cross  section  at 
the  first  station,  centre  height  C  =  10.2,  side  heights  ht  and  Jis  = 


36 

6.8  and  15.2,  and  side  distances  d  and  d'  =  17.2  and  29.8  ;  and  at 
second  station,  centre  height  38.6,  side  heights  28.6  and  53.0,  and 
side  distances  49.9  and  86.5. 

Calculation  of  areas  A  and  A',  and  correction  numbers  N  and  N'. 

s-\-s' 
For  the  grade  triangle  corresponding  to  Z»  «=  14  and  -    -  =  1£, 

tQ 

the  height  table  1  =  4.67,  and  the  area  table  2 •  =  33  =  a. 

By  Formula  (1)  and  Rule  1. 
Area  (A+«)  =  <iM±iM<lM±?M)  =  349  table  3  =  18.7  = 

</ 

correction  number  N;  and  349  —  33  =  316  —  A. 
Area(A'+«')  =  (38.6+4.67)(49.9+86.5) 

=  correction  number  N';  and  2951  —  33  =  2918  =  A'. 

Calculation  of  Contents. — Formula  (18),  Rule  1. 
316+2918 


1S.7~54.3  =  35.6  table  5 -782    " 

Contents  for  100  feet 5207  cyds. 

Test  by  Formula  13. 

From  the  preceding  data  the  notes  of  the  middle  area  would  give 
centre  height  24.4,  and  side  distances  33.55  and  58.15  ;  and  by  For 
mula  (1) 

(24.4  +  4.67)  (33.55+  58. 15)  v 

OL>   ^^    LOOO   O'J   ^^    1OUU   ^^   iVL. 

2 

i    17         i    /1.n3l7+29lS-hl300x4     100 
by  Formula  (13)  -  -— 2J  _  x  _  = 

To  find  the  equivalent  level  heights. — (Rule  7.) 
316  table  4. . .  .1170  table  10. . .  .10.6  equiv.  lev.  lit 
2918  table  4. . ..  10,807  table  10 ..  .39.7     " 

Test  by  Trautwine's  method,  with  level  heights. 

10.6  table  10 1174 

39.7  table  10 10,815 

(25.15  table  10. ...... .4818.5)x4 19,274 

6 [31, 263 
Contents  for  100  feet 5^210.5  cyds. 


37 


By  Formula  (21)  ,  Rule  (4),  with  level  heights. 

10-G+39-7  -  25.15  table  10.  .  .  .4818.5 

/& 

10.G~  39.7  =  29.1  table  15  .............  +392.0 

Contents  for  100  feet  ...........  5,210.5  cyds. 

By  Formula  (20),  with  eml  areas  and  level  heights. 
316+2918 


10.6~39.7  =  29.1  table  17  ...............  —784 

Contents  for  100  feet  ..............  5205  cyds. 

Approximation  ly  Formula  (20),  with  centre,  heights  of  profile  sub 
stituted  for  level  heights. 

=  1617  table  4  .................  5989 


/i 

10.2—38.6  =  28.4  table  17..  .  .—747 


Approximate  contents  for  100  feet..  5, 242  cyds. 

This  approximation  is  for  an  extreme  case,  as  in  practice  the 
difference  between  two  consecutive  centre  heights  is  rarely  as  much 
as  one-half  of  the  difference  above  taken.  In  ordinary  cases  this 
approximation  gives  results  very  nearly  correct. 

It  will  be  observed  that  by  Trautwine's  method,  as  given  above, 
three  quantities  are  taken  from  the  tables,  and  that  it  involves  an 
addition  of  three  quantities,  a  multiplication,  and  a  division  ;  whilst 
by  Rule  4,  which  with  the  same  data  gives  the  same  result,  the  sum 
of  two  quantities  taken  from  the  tables  is  the  required  contents. 

Example  6. — Correction  of  Contents  for  Curvature. — If  the 
second  cross  section  of  Example  5  is  at  the  middle  one  of  three 
stations  100  feet  apart,  and  all  of  them  on  a  G°  curve  which  is  con 
cave  toward  the  higher  ground,  the  correction  for  curvature  to  be 
deducted  at  the  station  under  consideration  is  obtained  as  follows  by 
Rule  5  : 

From  the  above  C°  =  G,  and  from  the  notes  of  Example  5, 
A+0  =  2951,  and  d~d'  =  3G.6.  But  3G.6  table  18  =  0.007885  ; 
and  Q  =  2951  x  6  x  0.007885  =  139.6  cyds. 

Test  l)y  IlencUs  Formula. 

C  =  \l,-c(d-d')+il)(h-h')}  X$(d+dr)  sin  D,  in  which  d  and  d' 
are  side  distances,  h  and  h'  side  heights,  c  the  centre  height,  and  D 


38 

die   deflection   angle  ;    hence   from   the   above   and   the   notes  of 
Example  5, 

=  3768.5  cu.  feet 


=  139.  G  cyds.     In  practice  d~d'  is  required  to  the  nearest  foot  only, 


REMARKS  OX  ESTIMATING  CONTENTS. 

PROFILE   EARTHWORK. 

In  addition  to  the  cross  sections  at  the  regular  stations,  others 
are  necessary  where  changes  begin  in  the  character  of  the  transverse 
surface  slope,  as  well  as  at  all  points  where  the  surface  line  of  the 
profile  changes  its  direction  ;  and  all  of  the  formulae  and  rules  here 
tofore  given  for  finding  the  contents  suppose  the  solid  to  be  between 
two  consecutive  cross  sections  taken  at  such  points. 

In  passing  from  cutting  into  embankment,  cross  sections  should 
always  be  taken  at  the  two  points  on  opposite  sides  of  the  road-bed 
where  the  cutting  "runs  out."  This  will  obviate  the  necessity  for 
staking  out  the  '•'  P.P."  except  with  a  zero  point  on  the  centre  line, 
as,  in  addition  to  accurate  data  for  calculation  of  the  pyramids  of 
cut  and  bank  which  lie  between  the  two  cross  sections  thus  taken, 
two  more  zero  points,  one  on  each  side  of  the  road-bed,  will  be 
given.  For  like  reasons,  in  passing  from  thorough  into  side  hill 
cutting,  the  point  on  the  lower  side  where  the  excavation  runs  out 
should  be  cross-sectioned. 

Where  the  original  quantities  of  excavation  and  embankment 
have  been  calculated,  and  the  work  is  being  done  according  to  the 
slope-stakes  and  field-notes,  probably  the  simplest  method  of  obtain 
ing  the  quantities  moved  in  an  unfinished  cutting  or  embankment 
is  to  take  the  average  heights  above  or  below  the  road-bed  at  each 
of  the  several  stations  of  that  portion  which  has  been  worked  upon, 
and  then,  with  Formula  (21),  Rule  4,  and  tables,  to  calculate  by 
these  heights  the  quantities  remaining  to  be  done.  The  latter  sub 
tracted  from  the  original  quantities  between  the  same  stations  will, 
of  course,  give  the  desired  amount. 

When  the  material  lies  in  strata,  a  similar  means  may  be  used 
for  determining  the  respective  quantities  of  the  different  kinds  of 


39 

excavation.  For  example,  a  cutting  may  be  composed  of  earth  at 
top,  loose  rock  below  the  earth,  and  solid  rock  at  bottom  :  the 
amounts  then  calculated  by  the  loose  rock  heights,  and  deducted 
from  the  original  quantities  giving  the  earth,  and  the  solid  rock- 
similarly  calculated  and  deducted  from  the  amounts  obtained  by  the 
loose  rock  heights  giving  the  loose  rock.  When  the  necessary  ave 
rage  heights  have  been  obtained,  the  quantities  corresponding  may 
be  found  very  rapidly  by  Rule  4  and  the  proper  tables. 

For  approximate  estimates,  when  the  centre  heights  and  trans 
verse  surface  slopes  only  are  given,  the  shortest  method  is  to  find  the 
equivalent  level  heights  by  Trautwine's  diagrams,  and  then  take  out 
the  contents  by  Rule  4. 

When  the  work  is  carried  on  irregularly,  no  general  rules  for 
ascertaining  the  true  contents  can  be  given.  When  the  cross  sections 
are  very  irregular  and  dissimilar,  the  best  practical  rule  is  to  take 
them  at  very  short  intervals.  This  in  all  cases  reduces  the  error  in 
the  calculation  of  contents  to  a  minimum. 

A  very  careful  and  thorough  investigation  of  the  mathematical 
methods  of  calculating  irregular  earthwork  is  given  in  the  article  on 
"  Earthwork  "  in  Henck's  "  Field-Book, "  and  to  that  the  theoretical 
reader  is  referred. 

BOREOW  PITS. 

For  obtaining  the  contents  of  extensive  borrow  pits,  the  follow 
ing  will  be  found  to  be  about  as  simple  a  method  as  is  consistent 
with  correctness.  Before  the  excavation  is  commenced,  lay  off  the 
surface  in  squares,  rectangles,  or  triangles,  small  enough  to  be  con 
sidered  as  plane  surfaces,  and  take  elevations  with  the  Level  at  all  of 
the  corners.  These  elevations  must  be  referred  to  a  base  which  will 
be  below  the  bottom  of  the  borrow  pit  when  the  work  is  finished. 

A  plan  of  the  ground  as  laid  off  should  then  be  made,  and  the 
elevations  above  the  base  recorded  on  it  at  the  corners.  When  r,n 
estimate  of  the  quantities  excavated  is  to  be  made  during  the  pro 
gress  of  the  work,  the  horizontal  limits  of  the  pit  as  then  excavated 
should  be  taken,  and  inside  of  these  limits  the  whole  of  the  ground 
again  divided  into  rectangles  and  triangles  without  reference  to  UK 
former  surface  divisions,  the  elevations  above  the  base  plane  again 
being  taken  at  all  corners,  including  those  on  the  surface  at  the 
edges  of  the  pit. 

The  original  quantity  inside  of  the  pit  limits  and  down  to  the 
base  plane,  taken  as  a  series  of  truncated  prisms,  should  then  be 
calculated,  and  next  the  quantity  remaining  inside  of  the  pit  limits 


40 

and  above  the  base  plane.  The  difference  between  those  amounts 
gives  the  quantity  excavated. 

The  advantage  of  using  an  independent  method  of  dividing  up 
the  ground  after  the  original  surface  has  been  removed  is  that  it 
rarely  happens  that  the  best  arrangement  of  these  subdivisions  for 
reducing  to  plane  surfaces  will  agree  accurately,  either  in  size  or 
position,  with  those  originally  taken  on  the  ground  surface.  If, 
however,  the  same  divisions  can  be  taken  in  the  bottom  of  the  pit  as 
originally  on  the  surface,  the  differences  of  the  elevations  at  each 
corner  taken  before  and  after  the  excavation  is  made  will  give  the 
heights  of  the  prisms,  of  which  the  contents  may  be  obtained  by  a 
single  calculation. 

In  order  to  prevent  the  necessity  for  recalculating  the  finished 
portions  at  each  estimate,  when  any  portion  of  the  pit  will  not  again 
be  disturbed,  its  limits  should  be  referenced  on  the  ground  and  indi 
cated  on  the  plan,  and  its  contents  recorded  separately, 


RULES  FOR  VARIOUS  USES  OF  TABLES. 

To  find  the  height  of  an  equivalent  level  section. 
*  Given  :  areas,  side  slopes,  and  base. 

RULE  7. 

Enter  table  4  with  the  given  area,  and  take  out  the  corresponding 
quantity  :  find  the  quantity  nearest  to  this  in  the  body  of  table  of 
level  cuttings  with  the  given  side  slopes  and  base,  and  the  index 
number  corresponding  is  the  equivalent  level  height  to  the  nearest 
tenth. 


*  When  centre  heights  and  transverse  surface  slopes  only  are  given,  if  r  = 
ratio  to  1  of  surface  slope  =  cotangent  of  surface  angle,  and  «'  =  8,  then  the 

equivalent  level  height  =  h=  (  e-f-  | — r—      _  L 

\      2*7  V1-**       to 


41 


Example.— Given  a  =  800  ;  -^-  =  H  ;  b  =  14 

800  table  4. . .  .2963  table  15. ..  .18.9  equiv.  lev.  lit. 
To  find  the  area  corresponding  to  a  level  height,  reverse  the  pro 
cess  of  Rule  7. 

To  find  the  middle  area  of  Rule  1. 

Given  :  N",  N',  and  a. 

RULE  8. 


Enter  table  3  with  — -£ — ,  and  take  out  the  quantity  correspond 
ing  ;  from  this  deduct  a,  and  the  remainder  is  the  middle  area. 
From  example  5,  page  36,  1ST  =  18.7  ;  K"'  =  54.3  ;  and  a  —  33. 
18.7-J-54.3  _  qft  -  f0Kirt  Q  IQQO 


1332  -  33  =  1299  =  M 

To  find  the  middle  area  of  Rule  2. 

Given  :  n  and  n'. 

RULE  9. 

Enter  table  3  with  — ~- ,  and  the  quantity  corresponding  is  the 

middle  area. 

Example. — With  similar  end  areas  4x25  =  100,   and  8x50  = 
400,  the  middle  area  is  6x37.5  —  225.     Here  n  =  10  and  n'  —  20, 

,  n-\-n       104-20  ,  ,,    0      ___       ,, 

and  — ^ —  =  — ~ —  =  lo  table  3  =  22o  —  M. 

To  find  the  middle  area  of  Rule  4. 

9—4—  ^' 

Given  :  h  and  h' ;  --—-  ;  and  b. 

RULE  10. 
Enter  the  table  of  level  cuttings  for  the  given  side  slopes  and 

base  with    ~|~    ,  and  take  out  the  corresponding  quantity  :  find  the 

quantity  nearest  to  this  in  the  body  of  table  4,  and  the  index  num 
ber  corresponding  is  the  middle  area. 

Example. — From  example  5,  page  36,  h  =  10.6  and  h'  —  39.7. 

1Q>6t39>7  =  25. 15  table  15 .... 4818  table  4 ....  1301. 
A 


42 

To  extend  the  Correction  Tables,  general  or  special. 
RULE  11. 

When  the  difference  of  the  correction  numbers,  or  of  the  level 
heights,  is  too  large  to  enter  the  table  with,  take  one-half  of  it,  and 
with  this  enter  and  take  out  the  corresponding  quantity,  which  mul 
tiplied  by  4  gives  the  correction  required  far  a  length  of  100 
feet. 

Examples. — In  table  5  the  correction  corresponding  to  32  is  632.1, 
which  multiplied  by  4  gives  2528.4,  the  correction  corresponding 
to  64. 

In  table  17,  the  correction  corresponding  to  12.2  is  68.9,  which 
multiplied  by  4  gives  275.6,  the  correction  corresponding  to  24.4. 

To  find  the  special  corrections  for  any  given  side  slopes  from  the 
general  correction  table.  • 

RULE  12. 

Enter  table  5  with  h~hr,  and  take  out  the  corresponding  quan 
tity  ;  for  the  'special  plus  corrections  multiply  this  by  the  quarter- 
sum  of  the  ratios  of  the  side  slopes  I  — ~~  1  ;  for  the  special  minus 

(s  i  y\ 
-§t-l«      The  corrections  so 

obtained  are  for  =  lengths  of  100  feet. 

Examples. — From  table  5  the  general  minus  correction   corre- 

s-\~s' 
spending  to  39.4  is  958.2,  and  the  plus  correction  for  ~~-  —  1J  is 

958.2  x  f  =  718.7  corresponding  to  39.4  table  17.     The  minus  cor- 

g  i  g; 
rection  for  '-    -  =  |-  is  958.2  x  J-  =  479.1  corresponding  to  39.4 

2 

table  14.     In  like  manner  with  ~—  =  |  the  plus  correction  for  39.4 

A 

<?   I  -g' 

=  958.2  x  0.1  =  95.8,  table  8  ;  and  with  -    -  =  1,  the  minus  cor- 

fy 

rections,  general  and  special,  are  the  same,  as  are  N~N'  and  h^h'. 
(See  table  5,  and  examples  1  and  2,  pages  31  and  33.) 


43 


EXPLANATIONS  OF  TABLES. 

Table  1  is  for  obtaining  the  height  of  the  grade  triangle.  To 
use  it,  find  the  half-sum  of  the  ratios  of  the  given  side  slopes  at  the 
top.  and  the  number  vertically  below,  and  on  the  same  line  with  the 
given  road-bed  width  in  the  left  column,  is  the  height  required. 

g       I        Qf 

Thus  with  1}  =  16  and  ~~~  =  f  the  height  corresponding  is  12.8. 

Table  2  contains  the  area  of  the  same  triangle.  It  is  used  with 
the  same  data  and  entered  in  the  same  way.  Thus  with  I  =  18  and 

9-Jo' 

-  :=  -|-  the  area  corresponding  =  a  =  162. 

/£ 

Table  3  gives  square  roots  to  tenths,  or  correction  numbers  of 
areas.  To  use  it,  find  in  the  body  of  the  table  the  number  nearest 
to  that  which  expresses  the  area  under  consideration,  and  the  figures 
on  the  same  horizontal  line  in  the  left  column  arc  the  whole  num 
bers,  and  that  immediately  above  it,  at  the  top  of  the  table,  the 
tenths  of  the  correction  number  required.  Thus  if  the  area  to 
intersection  of  side  slopes  is  2,000,  the  correction  number  N  is  4-4.7  : 
if  one  of  similar  end  areas  is  230,  the  correction  number  n  is  15.2. 

Table  4  is  for  finding  the  contents  for  100  feet  corresponding  to 
a  given  area.  The  left  column  contains  the  tens,  and  the  top  the 
units,  of  the  area.  In  the  body  of  the  table  are  the  corresponding 
contents  in  cubic  yards  for  lengths  of  100  feet.  In  the  short  table 
of  two  lines  prefixed,  the  contents -corresponding  to  the  tenths  of  the 
area  are  given,  and  these  when  required  are  to  be  added  to  the  con 
tents  taken  from  the  main  table.  Thus  the  contents  corresponding 
to  the  area  1872.7  are  6933.3+2.6  =  6935.9  cubic  yards. 

Table  5  is  for  obtaining  the  corrections  for  computations  by  ave 
rage  areas.  The  arithmetical  difference  between  the  correction 
numbers  is  to  be  found  in  whole  numbers  and  tenths  respectively,  in 
the  left  column  and  at  the  top  of  the  table,  and  the  number  corre 
sponding  in  the  body  of  the  table  is  the  correction  in  cubic  yards  for 
a  length  of  100  feet.  Thus  if  the  difference  of  the  correction  num 
bers  is  28.3,  the  correction  corresponding  is  494.4  cycls.  This 
correction  is  always  to  be  subtracted. 

The  Tables  of  Level  Cuttings  for  special  side  slopes  and  road-bed 
widths  give  the  cubic  yards  for  lengths  of  100  feet  corresponding  to 
the  different  heights,  of  which  the  whole  numbers  are  in  the  left 
column  and  the  tenths  at  top. 


44 

The  special  tables  of  plus  corrections  give  the  correction  for 
computation  by  averaging  equivalent  level  heights.  The  differences 
of  the  end  heights  in  feet  and  tenths  respectively  are  in  the  left 
column  and  at  top,  and  the  corresponding  corrections  for  lengths 
of  100  feet  in  the  body  of  the  table.  Care  must  be  taken  to  use  the 
correction  table  with  the  half  sum  of  the  side  slopes  the  same  as  that 
of  the  table  of  level  cuttings  of  which  the  contents  are  to  be  cor 
rected. 

The  special  tables  of  minus  corrections  give  the  corrections  for 
average  areas  when  entered  with  the  heights  of  equivalent  level  sec- 
dons.  The  side  slopes  of  the  table  must  be  the  same  as  those  of  the 
end  sections,  between  which  the  contents  are  to  be  corrected. 

When  the  tables  of  minus  corrections  for  special  slopes  are 
entered  with  the  differences  of  the  centre  heights  of  the  profile 
instead  of  those  of  the  equivalent  level  heights,  in  ordinary  ground 
:i  close  approximation  to  the  true  correction  is  obtained. 

For  the  special  plus  correction  tables  the  half-sum  of  the  side 
.slopes  is  indicated  at  the  top.  For  the  special  minus  corrections 
the  slopes  are  indicated  at  the  bottom  of  the  same  tables. 

Table  18  contains  factors  for  calculation  of  the  corrections  for 
curvature.  Its  use  is  explained  in  Rules  5  and  G. 


TABLE  tfo.  1. 

Roadbed  Width  in  Left  Column ;   half-sum  of  ratios  of  Side  Slopes 
at  Top ;  Height  of  Grade  Triangle  in  body  of  Table. 


i 

b 

i 

t 

1 

i 

5 

8 

1 
4 

8 

1 

H 

H 

If 

n 

2 

IO 

25 

20 

13.3 

IO 

8.0 

6.7 

5-7 

5 

44 

4.0 

3-6 

3-3 

2-5 

I2j  30 

24 

16.0 

12 

9.6 

8.0 

6.9 

6 

5-3 

4.8 

4-4 

4-0 

30 

14 

35 

28 

18.7 

14 

II.  2 

9-3 

8.0 

7 

6.2 

56 

5.1 

4-7 

3-5 

16 

40 

32 

21.3 

16 

12.8 

10.7 

9-1 

8 

7-1 

6.4 

5-8 

5,3 

4.0 

18 

45 

36 

24.0 

18 

144 

12.0 

10-3 

9 

8.0 

7-2 

6-5 

6.0 

4-5 

20 

50 

40 

26.7 

20 

16.0 

13-3 

11.4 

IO 

8-9 

8.0 

7-3 

6.7 

5-0 

22 

55 

44 

29-3 

22 

17.6 

14-7 

12.6 

ii 

9.8 

8.8 

8.0 

7-3 

5-5 

24 

60 

48 

32.0 

24 

19.2 

16.0 

13.7 

12 

10.7 

9-6 

87 

8.0 

6.0 

26 

65 

52 

34.7 

26 

20.8 

17-3 

14.9 

13 

EX.6 

10.4 

9-5 

8.7 

6.5 

28 

70 

56 

37-3 

28 

22.4 

18.7 

16.0 

14 

12.4 

II.  2 

10.2 

9-3 

7-o 

30 

75 

60 

40.0 

30 

24.0 

20.0 

17.1 

15 

13.3 

12.0 

10.9 

1O.O 

7-5 

4 

i 

t 

i 

5 

"8 

i 

I 

1 

H 

U 

if 

H 

2 

TABLE 


2. 


Roadbed  Width  in  Left  Column;  half-sum  of  ratios  of  Side  Slopes 
at  Top;  Area  of  Grade  Triangle  in  body  of  Table. 


CJ 

J 

£T 

4 

t 

i 

I 

1 

i 

1 

4 

H 

Jl 

H 

2 

10 

125 

100 

66.7 

50 

4O.O 

33-3 

28.6 

25 

22.2 

20.0 

18.2 

16.7 

12.5 

12 

180 

144 

96.0 

72 

57-6 

48.0 

41.1 

.36 

32.0 

28.8 

26.2 

24.0 

18.0 

M 

245 

196 

130.7 

98 

78.4 

65.3 

56.0 

49 

43,5 

.38.2 

35-6 

32.7 

24-5 

ib 

320 

2561170.7 

128 

102.4 

85-3 

73-i 

64 

56.9 

51-2 

46.6 

42.7 

32.0 

[8 

4°  5 

3241216.0 

162 

129.6 

108.0 

92.6 

81 

72.0 

64.8 

58.9 

54-0 

40.5 

20 

500 

400 

266.7 

200 

1  60.0 

133.3 

"4-3 

IOO 

88.9 

80.0 

72.7 

66.7 

50.0 

22  605 

484 

322.7 

242 

193.6 

161.3 

138.3 

121 

107.5 

96.8 

88.0 

80.7 

60.5 

24]  720 

576  384.0 

288 

230.4 

192.0 

164.6 

144 

128.0 

II5-2 

104.7 

96.0 

72.0 

26 

845 

676 

450.7 

338 

270.4 

225.3 

I93.I 

150.2 

135-2 

122.9 

112.7 

84,5 

28 

980 

784 

522.7 

392 

313-6 

261.3 

224.0 

196 

174.2 

156.8 

142.6 

130.7 

98.0 

30 

1125 

900 

600.0 

450 

360.0 

300.0 

257.1 

225 

200.0 

iSo.o 

163.6 

150.0 

112.5 

i 

i 

* 

* 

I 

1 

* 

1 

H 

H 

If 

H 

* 

46 


TABLE  tfo.  3. 

Areas  in  body  of  Table;   Correction  Nos.,  in  feet  and  tenths,  in  left 
column  and  at  top. 


u 

i 

Diff.to 

!£     0 

.1      .2 

-3 

•4     -5 

.6 

-7 

.8 

-9 

0.05 

°   o  j   o.o   o.o   o.i 

0.2 

0-3 

0.4 

*  0.5 

0.6 

0.8 

0.05 

1     I       1.2 

i-4 

i-7 

2. 

2-3 

2.6 

2.9 

3-2 

3-6 

0.2 

2 

4     4-4 

4.8 

5-3 

5.8 

6-3 

6.8 

7-3 

7.8 

8.4 

o-3 

3 

9 

9.6 

IO.2 

10.9 

n.6 

12.3 

13- 

13-7 

14.4 

15.2 

0.4 

4 

16 

16.8 

17-6 

18.5 

19.4 

20.3 

21.2 

22.1 

23.    24. 

o-5 

5 

25 

26. 

27- 

28.1 

29.2 

30-3 

31-4 

32-5 

33-6 

34-8 

0.6 

6 

36 

•37-2 

38.4 

39-7 

41. 

42-3 

43-6 

44-9 

46.2 

47-6 

0.7 

7 

49 

50.4 

51-8 

53-3 

54-8 

56.3 

57-8 

59-3 

60.8 

62.4 

0.8 

8 

64 

65.6 

67.2 

68.9 

70.6 

72.3 

74- 

75-7 

77-4 

79.2 

0.9 

9 

Si 

82.8 

84.6 

86.5 

88.4 

90-3 

92.2 

94.1 

96. 

98. 

io 

IOO 

IO2. 

104. 

1  06.  i 

108.2 

110.3 

112.4 

II4-5 

116.6 

118.8 

.1 

U 

121 

123.2 

125-4 

127.7 

130. 

132.3  134.6  |  136.9 

139.2 

141.6 

o 

12 

144 

146.4 

148.8 

I5I.3 

153-8 

156-3 

158.8 

161.3 

163.8 

166.4 

•3 

X3 

169 

I7I.6 

174.2 

176.9 

179.6 

182.3  185- 

187.7 

190.4 

193.2 

•4 

*4 

I96 

198.8 

2OI.6 

204.5 

207.4 

210.3 

213.2 

216.  i 

219. 

222. 

•  5 

15 

225 

228. 

231. 

234.1 

237-2 

240.3 

243.4!  246.5 

249.6 

252.8 

.6 

16 

256 

259.2 

262.4 

265.7 

269. 

272.3 

275.6 

278.9 

282.2 

285.6 

•  7 

J7 

289 

292.4 

295.8 

299-3 

302.8  306.3 

309.8 

3I3-3 

316.8 

320.4 

.8 

18 

324 

327.6   331.2 

334-9 

338.6  342.3 

346.   349-7 

353-4 

357-2 

•9 

*9 

361 

364.3 

368.6 

372-5 

376.4  380.3 

384.2  388.1 

392. 

396. 

2. 

20 

400 

404. 

408. 

412.1 

416.2  420.3 

424.4  428.5 

432.6 

436.8 

2.1 

21 

441 

445-2 

449-4 

453-7 

458. 

462.3 

466.6  |  4.70.9 

475-2 

479-6 

2.2 

22 

484 

488.4 

492.8 

497-3 

501.8 

506.3 

510.8  i  515.3 

519-8 

5244 

2-3 

23 

529 

533-6 

538-2 

542-9 

547-6 

552-3 

557-   561-7 

566.4 

57L2 

2-4 

24 

576 

580.8 

585-6 

59°-5 

595-4 

600.3 

605.2  i  610.1 

615. 

620. 

2-5 

25i  625 

630. 

635. 

640.1 

645.2 

650.3 

655-4 

660.5 

665.6 

670.8 

2.6 

26 

676 

681.2 

686.4 

691.7 

697. 

702.3 

707.6 

712.9 

718.2 

723-6 

2.7 

27 

729 

734-4 

739-8 

745-3 

750.8 

756.3 

761.8 

767-3 

772.8 

778.4 

2.8 

28 

784 

789.6 

795-2 

800.9 

806.6 

812.3 

818. 

823.7 

829.4 

835.2 

2-9 

29 

84I 

846.8 

852.6 

858-5 

864-4 

870.3 

876.2 

882.1 

888. 

894. 

3.0 

30 

900 

906. 

912. 

918.1 

924-2 

930.3 

936.4 

942-5 

948.6 

954-8 

3-i 

3i 

96l 

967.2 

973-4 

979-7 

986 

992-3 

998.6 

1005  jion 

1018 

3-2 

32 

1024 

1030 

1037  11043 

1050 

1056 

1063 

1069 

1076 

1082 

3.3 

33 

1089 

1096 

1102  jnog 

1116 

1122 

1129 

1136 

1142  '1149 

3-5 

34 

1156 

1163 

1170   1176 

1183 

1190 

1197 

1204 

I2II    1218 

3-6 

35 

1225 

1232 

1239   1246 

1253 

I26O 

1267 

1274 

1282 

1289 

3-6 

361296 

1303 

1310   1318 

1325 

1332 

1340 

1347 

1354 

1362 

3-7 

37  1369 

1376 

1384  |i39i 

1399 

1406 

1414 

1421 

1429 

1436 

3-8 

38 

1444   1452 

1459 

1467 

1475 

1482 

1490 

1498 

1505 

1513 

3-9 

39 

1521 

1529 

1537 

1544 

1552 

1560 

1568 

1576 

1584 

I592 

4.0 

40  1600 

r6o8 

1616 

1624 

1632 

1640 

1648 

1656 

1665 

i673 

4.1 

:  4l|l68l 

1689 

1697 

1706 

1714 

1722 

i73i 

1739 

1747 

1756 

4-2 

431764 

1772 

1781 

1789 

1798 

1806 

1815 

1823 

1832 

1840 

4.2 

4311849 

1858 

1866  . 

i875 

1884 

1892 

1  901 

1910 

I9l8 

1927 

4-3 

44  1936 

1945 

1954 

1962 

1971 

1980 

1989 

1998 

2007 

2016 

4.4 

452025   2034 

2043 

2052 

2061 

2O7O 

2079 

2088 

2098 

2107 

4-5 

462116   2125 

2134 

2144 

2153 

2162 

2172 

2181 

2190 

2  2OO 

4-7 

47^2209   2218 

2228 

2237 

2247 

2256 

2266 

2275 

2285 

2294 

4.8 

482304   2314 

2323 

2333 

2343 

2352 

2362 

2372 

238l 

2391 

4.8 

49  2401 

2411  '2421 

2430 

2440 

2450 

2460 

2470 

2480 

2490 

5-0 

502500 

2510   2520 

2530 

2540 

2550 

2560 

2570 

2581 

2591 

5-o 

0 

,     , 

-3     -4 

.5 

.6 

•7 

.8 

-9 

47 


TABLE  No.  3— CONCLUDED. 

Areas  in  body  of  Table;  Correction  JVbs.,  in  fed  and  tenths,  in  left 

column  and  at  top. 


«i 

D  iff.  for 

1 

o 

.1 

.2 

.3 

•4 

•5 

.0 

•7 

.8 

•9 

0.05 

51 

2601 

2611 

2621 

2632 

2642 

2652 

2663 

2673 

2683 

2694 

5-2 

52 

2704 

2714 

2725 

2735 

2746 

2756 

2767 

2777 

2788 

2798 

^.2 

53 

2809 

2820 

2830 

2S4r 

2852 

2862 

2873 

2884 

2894 

2905 

5-3 

54 

2916 

2927 

2938 

2948 

2959 

2970 

2981 

2992 

3003 

3014 

5-4 

55 

3025 

3036 

3047 

3058 

3069 

3080 

3091 

3102 

3H4 

3125 

5-5 

56 

3136 

3147 

3158 

3170 

3181 

3192 

3204 

3215 

3226 

3238 

5-7 

57 

3249 

3260 

3272 

3283 

3295 

3306 

33i8 

3329 

3341 

3352 

5-7 

58 

3364 

3376 

3387 

3399 

34ii 

3422 

3434 

3446 

3457 

3469 

5-8 

59 

343i 

3493 

3505 

35r6 

3528 

3540 

3552 

3564 

3576 

3583 

5-9 

60 

3600 

3612 

3624 

3636 

3648 

3660 

3672 

3684 

3697 

3709 

6.0 

61 

3721 

3733 

3745 

3753 

3770 

3782 

3795 

3807 

3819 

3832 

6.2 

62 

3S44 

3856 

3869 

3881 

3894 

3906 

39J9 

3931 

3944 

3956 

6.2 

63 

3969 

3982 

3994 

4007 

4020 

4032 

4045 

4058 

4070 

4083 

6-3 

64 

4096 

4109 

4122 

4134 

4147 

4160 

4173 

4186 

4199 

4212 

6.4 

65 

4225 

4238 

4251 

4264 

4277 

4290 

4303 

4316 

4330 

4343 

6-5 

66 

4356 

4369 

4382 

439^ 

4409 

4422 

4436 

4449 

4462 

4476 

6-7 

67 

4489 

4502 

45i6 

4529 

4543 

4556 

4570 

4583 

4597 

4610 

6.7 

68 

4624 

4638 

4651 

4665 

4679 

4692 

4706 

4720 

4733 

4747 

6.8 

69 

4761 

4775 

4789 

4802 

4816 

4830 

4844 

4858" 

4872 

4886 

6.9 

70 

4900 

4914 

4928 

4942 

4956 

49/0 

4984 

4998 

5013 

5027 

7.0 

71 

5041 

5055 

5069 

5084 

5098 

5112 

5127 

5i4i 

5155 

5170 

7.2 

72 

5*84 

5198 

5213 

5227 

5242 

5256 

5271 

5285 

53oo 

5314 

7.2 

73 

5329 

5344 

5358 

5373 

5388 

5402 

5417 

5432 

5446 

546i 

7-3 

74 

5476 

5491 

5506 

5520 

5535 

5550 

5565 

558o 

5595 

5610 

7-4 

75 

5625 

5640 

5655 

5670 

5685 

5/00 

5715 

5730 

5746 

576i 

7-5 

76 

5776 

5791 

5806 

5822 

5837 

5852 

5868 

5883 

5898 

59*4 

7-7 

77 

5929 

5944 

5960 

5975 

5991 

6006 

6022 

6037 

6053 

6068 

7-7 

78 

6084 

6100 

6115 

6131 

6147 

6162 

6178 

6194 

6209 

6225 

7-8 

79 

6241 

6257 

6273 

6288 

6304 

6320 

6336 

6352 

6368 

6384 

7-9 

80 

6400 

6416 

6432 

6448 

6464 

6480 

6496 

6512 

6529 

6545 

8.0 

81 

6561 

6577 

6593 

6610 

6626 

6642 

6659 

6675 

6691 

6708 

8.2 

82 

6724 

6740 

6/57 

6773 

6790 

6806 

6823 

6839 

6856 

6872 

8.2 

83 

6889 

6906 

6922 

6939 

6956 

6972 

6989 

7006 

7022 

7039 

8-3 

84 

7056 

7073 

7090 

7106 

7123 

7140 

7157 

7174 

7191 

7208 

8.4 

85 

7225 

7242 

7259 

7276 

7293 

73io 

7327 

7344 

7362 

7379 

8-5 

86 

7396 

7413 

7430 

7448 

7465 

7482 

7500 

7517 

7534 

7552 

8.6 

87 

7569 

7586 

7604 

7621 

7639 

7656 

7674 

7691 

7709 

7726 

8-7 

88 

7744 

7762 

7779 

7797 

7815 

7832 

7850 

7868 

7885 

79°3 

8.8 

89 

7921 

7939 

7957 

7974 

7992 

8010 

8028 

8046 

8064 

8082 

8.9 

go 

Sioo 

8nS 

81,36 

8i54 

8172 

8190 

8208 

8226 

8245 

8263 

9.0 

Qi 

8281 

8299 

8317 

8336 

8354 

83/2 

8391 

8409 

8427 

8446 

9.2 

92 

8464 

8482 

8501 

8519 

8538 

85^6 

8575 

8593 

8612 

8630 

9.2 

03 

8649 

8568 

8686 

8/05 

8724 

8742 

8761 

8780 

8798 

8817 

9-3 

-*J 
94 

8836 

8855 

8874 

8892 

8911 

8930 

8949 

8968 

8987 

9006 

9-4 

95 

9025 

9044 

9063 

9082 

9101 

9120 

9139 

9158 

9178 

9197 

9-5 

96 

9216 

9235 

9254 

9274 

9293 

9312 

9332 

9351 

93/0 

939° 

9.6 

97 

9409 

9428 

9448 

9467 

9487 

9506 

9526 

9545 

9565 

9584 

9-7 

98 

9604 

9624 

9643 

9663 

9683 

9702 

9722 

9742 

9761 

9781 

9.8 

99 

9801 

9821 

9841 

9860 

9880 

9900 

9920 

9940 

9960 

9980 

9-9 

100 

IOOOO 

IOO2O 

10040 

10060 

10080 

IOIOO 

IOI20 

10140 

10161 

10181 

IO.O 

0 

.x 

.2 

•3 

•4 

•5 

.5 

•7 

.8 

•9 

48 
TABLE  No.  4. 


Areas  

O  I 

O  2 

O  2^ 

O  1 

O  d. 

O  ^ 

06 

O  7 

o  ?e; 

08 

o  o 

Contents.  . 

O.d 

O.7 

o.o 

I.I 

I  e, 

I.O 

2  2 

a.6 

2.8 

to 

1.1 

Areas  :  Tens  in  left  Column  and  Units  at  top..     Contents  for  100  feet 
in  cubic  yards  in  body  of  Table. 


1 

O.O 

I.O 

2.0 

3-o 

4.0 

5-o 

6.3 

7.0         8.0 

g.o 

o 

0.0 

3-7 

74 

n.  i 

I4.8 

18.5 

22.2 

25-9 

29.6 

33-3 

I 

37- 

40.7 

44-4 

48.1 

5L9 

55-6 

59-3 

63- 

66.7 

70.4 

2 

74.1 

77-8 

81.5 

85.2 

88.9 

92.6 

96.3 

IOO. 

103.7 

107.4 

3 

in.  i 

114.8 

118.5 

122.2 

125.9 

129.6 

133-3 

137. 

140.7 

144.4 

4 

148.1 

"151-9 

155-6 

159-3 

I63. 

166.7 

170.4 

174.1 

177.8 

181.5 

5 

185.2  |    188.9 

192.6 

196.3 

200. 

203.7 

2074 

211.  1 

214.8 

218.5 

6 

222.2 

225.9 

229.6 

233-3 

237- 

240.7 

244.4 

248.1 

251-9 

255.6 

7 

259-3 

263. 

266.7 

270.4 

274.1 

277.8 

281.5 

285.2 

288.9 

292.6 

8 

296.3 

300. 

303-7 

307.4 

311.  1 

314.8 

3i8.5 

322.2 

325-9 

329-6 

9 

333-3 

337- 

340.7 

344-4 

348.1 

'  351-9 

355-6 

359-3 

363- 

366.7 

10 

370.4 

374-1 

377-8 

38i.5 

385.2 

388.9 

392-6 

396.3 

400. 

403.7 

ii 

407.4 

411.1 

414.8 

418.5 

422.2 

425-9 

429.6 

433-3 

437- 

440.7 

12 

444-4 

448.1 

451-9 

455-6 

459-3 

463- 

466.7 

470.4 

474-1 

477.8 

*3 

481.5 

485.2 

488.9 

492.6 

496.3 

500. 

503-7 

5074 

511.1 

514-8 

J4 

518.5 

522.2 

525-9 

529.6 

533-3 

537- 

540.7 

544-4 

548.1 

551-9 

15 

555-6 

559-3 

563- 

566.7 

570.4 

574-1 

577-8 

58i.5 

585-2 

588.9 

16 

592.6 

596-3 

600. 

603.7 

607.4 

6n.i 

614.8 

618.5 

622.2 

625.9 

X7 

629.6 

633.3 

637. 

640.7 

644.4 

648.1 

651.9 

655.6 

659-3 

663. 

18 

666:7 

670.4 

674.1 

677-8 

681.5 

685.2 

688.9 

692.6 

696.3 

700. 

*9 

703-7 

707.4 

711.1 

714.8 

718.5 

722.2 

725-9 

729.6 

733-3 

737- 

20 

740.7 

744-4 

748.1 

751-9 

755-6 

759-3 

763. 

766.7 

770.4 

774-1 

21 

777-8 

78i.5 

785.2 

788.9 

792.6 

796.3 

800. 

803.7 

807.4 

8n.i 

22 

814.8 

818.5 

822.2 

825.9 

829.6 

833.3 

837. 

840.7 

844.4 

848.1 

23 

851.9 

855-6 

859-3 

863. 

866.7 

870.4 

874.1 

877-8 

881.5 

885.2 

24 

888.9 

892.6 

896.3 

900. 

9°3-7 

907.4 

911.1 

914.8 

918.5 

922.2 

2S 

925-9 

929.6 

933-3 

93^. 

940-7 

944-4 

948.1 

951-9 

955-6 

959-3 

26 

963- 

966.7 

970.4 

974.1 

977.8 

981.5 

985-2 

988.9 

992.6 

996.3 

27 

IOOO. 

1003.7 

1007.4 

ion.  i 

1014.8 

1018.5 

IO22.2 

1025.9 

1029.6 

1033-3 

28 

1037. 

1040.7 

1044.4 

1048.1 

1051.9 

1055.6 

1059.3 

1063. 

1066.7 

1070.4 

29 

1074.1 

1077.8 

1081.5 

1085.2 

1088.9 

1092.6 

1096.3 

I  IOO. 

1103.7 

1107.4 

30 

IIII.  I 

1114.8 

1118.5 

II22.2 

1125.9 

1129.6 

1133-3 

II37- 

1140.7 

1144.4 

3i 

1148.1 

1151.9 

II55-6 

II59-3 

1163. 

1166.7 

1170.4 

1174.1 

1177.8 

1181.5 

32 

1185.2 

1188.9 

1192.6 

1196.3 

1200. 

1203.7 

1207.4 

I2II.I 

1214.8 

1218.5 

33 

1222.2 

1225.9 

1229.6 

1233-3 

1237. 

1240.7 

1244.4 

I248.I 

1251-9 

1255-6 

34 

1259-3 

1263. 

1266.7 

1270.4 

I274.I 

1277.8 

1281.5 

1285.2 

1288.9 

1292.6 

35 

1296.3 

1300. 

I303-7 

1307.4 

I3II.I 

1314-8 

1318.5 

1322.2 

13259 

1329.6 

36 

1333-3 

1337- 

1340.7 

1344-4 

I348.I 

I35I.9 

1355-6 

1359-3 

1363- 

1366.7 

37 

1370.4 

I374-I 

1377-8 

I38I.5 

1385.2 

1388.9 

1392-6 

1396.3 

1400. 

I403-7 

38 

1407.4 

1411.1 

1414.8 

1418.5 

1422.2 

1425.9 

1429.6 

1433-3 

1437- 

1440.7 

39 

14444 

1448.1 

I45L9 

1455-6 

1459-3 

1463. 

1466.7 

1470.4 

I474-I 

1477.8 

40 

I48I.5 

1485-2 

1488.9 

1492.6 

1496.3 

1500. 

1503-7 

15074 

1511.1 

1514-8 

4i 

I5I8.5 

1522.2 

1525-9 

1529.6 

1533-3 

1537- 

15407 

1544-4 

1548.1 

I55L9 

42 

1555-6 

1559-3 

1563. 

1566.7 

1570.4 

I574-I 

1577-8 

1581.5 

1585-2 

1588.9 

43 

1592.6 

1596-3 

1600. 

1603.7 

1607.4 

i6n.i 

1614.8 

1618.5 

1622.2 

1625.9 

44 

1629.6 

1633-3 

1637. 

1640.7 

1644.4 

1648.1 

1651.9 

1655.6 

1659-3 

1663. 

45 

1666.7 

1670.4 

1674.1 

1677.8 

1681.5 

1685.2 

1688.9 

1692.6 

1696.3 

1700. 

46 

1703.7 

1707.4 

1711.1 

I7I4.8 

I7I8.5 

1722.2 

1725-9 

1729.6 

1733-3 

1/37. 

47 

1740.7 

1744.4 

1748.1 

I75L9 

1755-6 

1759-3 

1763. 

1766.7 

1770.4 

1774.1 

48 

1777-8 

1781.5 

1785.2 

1788.9 

1792.6 

1796.3 

1800. 

18037 

1807.4 

iSii.i 

49 

1814.8 

1818.5 

1822.2 

1825.9 

1829.6 

1833.3 

1837. 

1840.7 

1844.4 

1848.1 

50 

1851.9 

1855.6 

1859-3 

1863. 

1866.7 

1870.4 

1874.1 

1877.8 

1881.5 

1885.2 

O. 

«' 

2. 

3- 

,     |      5- 

6. 

7- 

8. 

9- 

49 
TABLE  ]So.  4— CONTINUED. 


Areas  

O.I 

O.2 

O.25  1    O.3 

0.4 

O.5 

0.6 

O.7  I    O.75 

08 

0.9 

Contents  

0.4 

0.7 

O.g     1    I.I 

1-5 

1.9 

2*2 

2.6  1    2.8 

3-0 

3-3 

Areas :  Tens  in  left  Column  and  Units  at  top.     Contents  for  WO  feet 
in  cubic  yards  in  body  of  Table. 


! 

0. 

I. 

2. 

3. 

4- 

5. 

6. 

I 

7- 

8. 

9- 

51 

1888.9 

1892.6 

1896.3 

1900. 

1903.7 

1907.4  1911.1 

1914.8 

1918.5 

1922.2 

52 

1925.9 

1929.6 

1933-3 

I937- 

1940.7 

1944.4 

1948.1 

1951-9 

1955-6 

1959-3 

53 

1963. 

1966.7 

1970.4 

1974.1 

1977.8 

1981-5 

1985-2 

1988.9 

1992.6 

1996.3 

54 

2OOO. 

2003.7 

20074 

2011.  1 

2014.8 

2018.5 

2O22.2 

2025.9 

2029.6 

2033.3 

55 

2037. 

2040.7 

2044.4 

2048.1 

2051.9 

2055.6 

2059.3 

2063. 

2066.7 

2070.4 

56 

2074.1 

2077.8  I  2081.5 

2085.2 

2088.9 

2092.6  j  2096.3 

2IOO. 

2103.7 

2107.4 

57 

2II1.I 

2114.8 

2II8.5 

2122.2 

2125.9 

2129.6 

2133-3 

2137. 

2140.7 

2144.4 

58 

2I48.I 

2151.9 

2155-6 

2159-3 

2163. 

2166.7 

2170.4 

2I74.I 

2177.8 

2181.5 

59 

2185.2 

2188.9 

2192.6 

2196.3 

2200. 

2203.7 

22074 

22II.I 

2214.8 

2218.5 

60 

2222.2 

2225.9 

2229.6 

2233.3 

2237. 

2240.7 

2244.4 

2248.1 

2251.9 

2255.6 

01 

2259-3 

2263. 

2266.7 

2270.4 

2274.1 

2277.8 

22SI.5 

2285.2 

2288.9 

2292.6 

62 

2296.3 

2300. 

2303.7 

2307.4 

23H.I 

2314-8 

2318.5 

2322.2 

2325-9 

2329.6 

63 

2333-3 

2337- 

2340.7 

2344-4 

2348.1 

235L9 

2355-6 

2359-3 

2363- 

2366.7 

64 

2370.4 

2374-1 

2377-8 

2381.5 

2385.2 

2388.9 

2392.6 

2396.3 

2400y 

2403.7 

65 

2407.4 

2411.1 

2414.8 

2418.5 

2422.2 

2425.9 

2429.6 

2433-3 

2437. 

2440.7 

66 

2444.4 

2448.1 

245L9 

2455-6 

2459-3 

2463. 

2466.7 

24/0.4 

2474.1 

2477-8 

67 

2481.5 

2485-2 

2488.9 

2492.6 

2496.3 

2500. 

2503.7 

2507-4 

2511.1 

2514-8 

68 

2513.5 

2522.2 

2525.9 

2529.6 

2533-3 

2537- 

2540.7 

2544-4 

2548.1 

2551-9 

69 

2555-6 

2559-3 

2563. 

2566.7 

2570.4 

2574-T 

2577-8 

25SI.5 

2585.2 

2588.9 

7° 

2592.6 

2596-3 

26OO. 

2603.7 

2607.4 

2611.1 

2614.8 

26l8.5 

2622.2 

2625.9 

71 

2629.6 

2633.3 

2637. 

2640.7 

2644.4 

2648.1 

2651.9 

2655.6 

2659-3 

2663. 

72 

2666.7 

2670.4 

2674.1 

2677.8 

2681.5 

2685.2 

2688.9 

2692.6 

2696.3 

2700. 

73 

2703.7 

2707.4 

27II.I 

2714.8 

2/18.5 

2722.2 

2725.9 

2729.6 

2733.3 

2737- 

74 

2740.7 

2744-4 

2748.1 

2751.9 

2755-6 

2759-3 

2763- 

2766.7 

2770.4 

2774-1 

75 

2777.8 

2781.5 

2785.2 

2788.9 

2792.6 

2796-3 

2800. 

2803.7 

2807.4 

2811.1 

76 

2814.8 

2818.5 

2822.2 

2825.9 

2829.6 

2833-3 

2837. 

2840.7  2844.4 

2848.1 

77 

2851.9 

2855.6 

2859-3 

2863. 

2866.7 

2870.4 

2874.1 

2877.8 

2881.5 

2885.2 

78 

2888.9 

2892.6 

2896.3 

2gOO. 

2903.7 

2907.4 

29II.I 

2914.8 

2918.5 

2922.2 

79 

2925.9 

2929.6 

2933-3 

2937- 

2940.7 

29444 

2948.1 

2951.9 

2955.6 

2959.3 

80 

2963. 

2966.7 

2970.4 

2974.1 

2977.8 

2981.5 

2985.2 

2988.9 

2992.6 

2996.3 

81 

3000. 

3003.7 

30074 

3OII.1 

3014.8 

3018.5 

3O22.2 

3025.9 

3029.6 

3033-3 

!  82 

3037. 

3040.7 

3044-4 

3048.1 

305L9 

3055-6 

3059-3 

3063. 

3066.7 

3070.4 

83 

3074-I 

3077.8 

30SI.5 

3085.2 

3088.9 

3092.6 

3096.3 

3100. 

3103.7 

3107.4 

84 

3IH.I 

3H4.8 

3II8.5 

3122.2 

3125.9 

3129-6 

3133.3 

3137.   3140.7 

31444 

85 

3I43.I 

3I5I9 

3155.6 

3I59.3 

3163. 

3166.7 

31/0.4 

3I74.I  3177.8 

3181.5 

86 

3185.2 

3188.9 

3192.6 

3196.3 

3200. 

3203.7 

32074 

32II.I 

3214.8 

3218.5 

87 

3222.2 

3225.9 

3229.6 

3233.3 

3237. 

3240.7 

32444 

3248.1 

3251.9 

3255-6 

88 

3259-3 

3263. 

3266.7 

3270.4 

3274.1 

3277.8 

32SI.5 

3285.2  3288.9 

3292.6 

89 

3296.3 

3300. 

3303.7 

3307-4 

33H.  I 

3314.8 

3318.5 

3322.2  3325.9 

3329.6 

go 

3333-3 

3337- 

3340.7 

3344-4 

3348.1 

335L9 

3355-6 

3359-3  i  3363. 

3366.7 

9* 

3370-4 

3374-1 

3377-8 

3381.5 

3385.2 

3388.9 

3392.6 

3396.3 

3400. 

3403.7 

92 

3407-4 

3411.1  3414.8 

3418.5 

3422.2 

3425.9 

3429-6 

3433-3 

3437. 

3440.7 

93 

3444-4 

3448.1 

3451-9 

3455-6 

3459-3 

3463. 

34667 

3470.4 

3474.1 

3477-8 

94 

34Sr.5 

3485.2 

3488.9 

3492.6 

3496.3 

3500. 

3503.7 

35074 

35U-I 

3514.8 

95 

3518.5 

3522.2 

3525.9 

3529-6 

3533-3 

3537- 

3540.7 

3544-4 

3548.1 

3551-9 

96 

3555-6 

3559-3 

3563. 

3566.7 

3570.4 

3574-1 

3577-8 

35SI.5 

3585-2 

3588.9 

97 

3592.6 

3596.3 

3600. 

3603.7 

3607.4 

3611.1 

3614.8 

3618.5 

3622.2 

3625.9 

98 

3629.6 

3633.3  3637. 

3640.7 

3644.4 

3648.1 

365I-9 

3655.6  3659-3 

3663. 

99 

3666.7 

3670.4 

3674.1  3677.8 

3681.5 

3635.2 

3688.9  i  3692.6  3696-3 

37oo. 

100  3703.7  | 

37074 

3711.1  3714.8 

3718.5 

3722.2 

3/25.9  3729.6 

3733-3 

3737- 

o. 

*.  1   3- 

4- 

i 
5-     6. 

7-     8. 

9- 

1 

i                 i 

I 

50 

TABLE  No.  4— CONTINUED. 


Areas  .  .  . 

O  I 

O  2 

O  2^ 

O  "? 

O  A 

Oe 

o  6 

O  7 

O  If, 

o  8 

OQ  ' 

0.9, 

Contents.  . 

O.A 

0.7 

o.o 

I.I 

1.< 

I.O 

2  2 

^6 

2.8 

TO 

** 

Areas:  Tens  in  left  Column  and  Units  at  top.      Contents  for  IQQfcet 
in  cubic  yards  in  body  of  Table. 


L 

o. 

I. 

2. 

3- 

4- 

5- 

6. 

• 

7- 

8.    9- 

XOI 

3740.7 

37444 

3748.1 

375T-9 

3755-6 

37593 

3763. 

3766.7 

37704 

3774-J 

102 

3777-8 

3781.5 

3785-2 

3788.9 

3792.6 

3796-3 

3800. 

3803.7 

3807.4 

3811.1 

103 

3814-8 

3818.5 

3822.2 

3825-9 

3829.6 

3833-3 

3837. 

3840.7 

3844.4  i  3848,1 

1104 

3851-9 

3855.6 

3859.3 

3863. 

3866.7 

3870.4 

3874-1 

3877-8 

3881.5  3885.2 

'1105 

3888.9 

3892.6 

3896.3 

3900. 

3903.7 

3907-4 

3911.1 

3914.8 

3918.5  3922,2 

100 

3925-9 

3929.6 

3933-3 

3937- 

3940.7  3944.4 

3948.1 

3951-9 

3955-6  3959-3 

107 

303- 

3966.7 

39704 

3974-1 

3977-8 

398i.5 

3985.2 

3988.9 

3992-6 

3996.3 

108 

4000. 

4003.7 

4007.4 

4011.1 

4014.8 

4018.5 

4022.2 

4025.9 

4029.6 

4033.3 

109 

4037. 

4040.7 

40444 

4048.1 

4051.9 

4055.6 

4059-3 

4063. 

4066.7 

4070.4 

no 

4074.1 

4077.8 

4081.5 

4085.2 

4088.9 

4092.6 

4096.3 

4100. 

4103.7 

4107.4 

III 

4111.1 

4114.8 

4II8.5 

4122.2 

4125.9 

4129.6 

4I33.3 

4I37. 

4140.7 

4144.4 

112 

4148.1 

4I5I-9 

4155.6 

4I59-3 

4163. 

4166.7 

4170.4 

4174.1 

4177.8 

4181.5. 

"3 

4185.2 

4188.9 

4192.6 

4196.3 

4200. 

4203.7 

4207.4 

4211.1 

4214.8 

4218.5 

114 

4222.2 

4225.9 

4229.6 

4233-3 

4237. 

4240.7 

4244.4 

4248.1 

4251.9 

4255.6 

H5 

4259-3 

4263. 

4266.7 

4270.4 

4274.1 

4277.8 

4281.5 

4285.2 

4288.9 

4292.6 

116 

4296.3 

4300. 

4303.7 

43074 

4311.1 

43I4.8 

4318.5 

4322.2 

4325.9 

4329-6 

117 

4333-3 

4337- 

4340-7 

43444 

4348.1 

4351-9 

4355-6 

4359-3 

4363. 

4366.7 

118 

43704 

4374-1 

4377-8 

4381.5 

4385-2 

4388.9 

4392-6 

4396.3 

4400. 

4403.7 

119 

4407.4 

4411.1 

4414.8 

4418.5 

4422.2 

4425.9 

4429.6 

4433-3 

4437. 

4440.7 

120 

4444-4 

4448.1 

4451-9 

4455-6 

4459-3 

4463- 

4466.7 

4470.4 

4474-1 

4477.8 

121 

4481.5 

4485-2 

4488.9 

4492.6 

4496.3 

4500. 

4503.7 

45074 

45H.I 

4514.8 

122 

4518.5 

4522.2 

4525-9 

4529-6 

4533-3 

4537- 

4540-7 

45444 

4548-1 

4551-9 

123 

4555-6 

4559-3 

4563. 

4566.7 

45704 

4574-1  4577-8 

458i.5 

4585-2 

4588.9 

124 

4592-6 

4596.3 

4600. 

4603.7 

4607.4 

4611.1  4614.8 

4618.5 

4622.2 

4625.9 

125 

4629.6 

4633-3 

4637. 

4640.7 

4644-4 

4648.1  4651.9 

4655-6 

4659-3 

4663. 

125 

4666.7 

4670.4 

4674.1 

4677.8 

4681.5 

4685.2  4688.9 

4692.6 

4696.3 

4700. 

127 

4703.7 

47074 

4711.1 

4714.8 

47i8.5 

4722.2  4725.9 

4729.6 

4733-3 

4737- 

128 

4740.7 

47444 

4748.1 

4751-9 

4755-6 

4759-3  4763. 

4766.7 

4770-4 

4774-1 

129 

4777-8 

4/81.5 

4785.2 

4788.9 

4792.6 

4796.3  4800. 

4803.7 

4807.4 

4811.1 

130 

4814.8 

4818.5 

4~822.2 

4825.9 

4829.6 

4833.3  4837. 

4840.7 

4844-4 

4848.1 

131 

4851.9  4855-6 

4859-3 

4863. 

4866.7 

4870.4  4874.1 

4877.8 

4881.5 

4885.2 

132 

4888.9 

4892.6 

4896.3 

4900. 

4903.7 

49074 

4911.1 

4914.8 

49l8-5 

4922.2 

133 

4925-9 

4929.6 

4933-3 

4937- 

4940.7 

49444 

4948.1 

4951-9 

4955-6 

4959-3 

134 

4963- 

4966.7 

4970.4 

4974.1 

4977-8 

498i.5 

4985.2 

4988.9 

4992.6 

4996.3 

135 

5000. 

5003.7 

5007.4 

5011.1 

5014.8 

5018.5 

5022.2 

5025.9 

5029.6 

5033.3 

136 

5037- 

5040.7 

5044.4 

5048.1 

5051-9 

5055-6 

5059.3 

5063. 

5066.7 

5070.4 

J37 

5074-1 

5077.8  5081.5 

5085.2 

5088.9 

5092.6 

5096.3 

5100. 

5103.7 

5107.4 

138 

$111.1 

5114-8 

5H8.5 

5122.2 

5I25-9 

5129.6 

5133.3 

5I37. 

5140.7 

51444 

139 

5148.1 

5I5L9 

5I55-6 

5I59-3 

5163- 

5166.7 

51704 

5I74-I 

5177.8 

5181.5 

140 

5185.2 

5188.9 

5192-6 

5196.3 

5200. 

5203-7 

5207.4 

5211.1 

5214-8 

5218.5 

141 

5222.2 

5225.9 

5229.6 

5233.3 

5237. 

5240.7 

52444 

5248.1 

5251-9 

5255-6 

142 

5259.3 

5263. 

5266.7 

52704 

5274-1 

5277.8 

5281.5 

5285.2 

5288.9 

5292.6 

143 

5296.3 

5300. 

5303.7 

53074 

53II-I 

5314.8 

53i8.5 

5322.2 

5325.9 

5329-6 

144 

5333-3 

5337- 

5340-7 

5344-4 

5348.1 

5351-9 

5355-6 

5359-3 

5363. 

5366.7 

*45  5370-4 

5374-1 

5377-8 

5381.5 

5385.2 

5388.9 

5392-6 

5396.3 

5400. 

5403.7 

146  5407.4  54H.I 

5414-8 

5418.5 

5422.2 

5425.9 

5429-6 

5433-3 

5437- 

5440.7 

147  54444  5448.1  5451-9 

5455-6 

5459-3 

5463- 

5466.7 

54704 

5474-1 

5477-8 

148  5481.5 

5485-2 

5488.9 

5492.6 

5496.3 

5500. 

5503-7 

55074 

55II-I 

5514-8 

149  5513.5  5522.2 

5525.9 

5529-6 

5533-3 

5537- 

5540-7 

55444 

554S.I 

5551-9 

150  5555-6  !  5559-3  55^3- 

5566.7 

55704 

5574-1 

5577-8 

5581.5 

5585.2 

5588.9 

j      | 

1 

o. 

I  . 

2. 

3. 

4. 

5- 

6. 

7. 

8. 

9- 

51 
TABLE  Xo.  4— CONTINUED. 


Areas. 


Contents. 


0.4 

o. 

0.25    03 


0.9 


0.4 
15 

0.5 

0.6 

0.7  j  0.75 

0.8 

0.9 
3-3 

1.9  |    22 

2.6  I    2.8 

30 

Areas  :  Tens  in  left  Column  and  Units  at  top.      Contents  for  100  feet 
in  cubic  yards  in  body  of  Table. 


+s 

I 

Jj 

o. 

i. 

2. 

3- 

4. 

5- 

6. 

7- 

8. 

9- 

151 

5592.6 

5596.3 

5600. 

5603.7 

5607.4 

5611.1 

5614-8 

5618.5 

5622.2 

5625.9  i 

152 

5629.6 

5633-3  5637- 

5640.7 

56444 

5648.1 

5651-9 

5655-6 

5659.3 

5663. 

153 

5666.7 

5670.4  5674-1 

5677-8 

5681.5 

5685.2 

5688.9 

5692.6 

5696.3 

5700. 

154 

5703.7 

57074 

57H.I 

5714-8 

5718.5 

5722.2 

5725.9 

5729-6 

5733-3 

5737- 

155 

5740.7 

5744.4  5748.1 

5751-9 

5755-6 

5759-3 

5763. 

5766.7 

5770.4 

5774-1 

156 

5777.8 

5781.5  5785.2 

5788.9 

5792.6 

5796.3 

5800.   5803.7 

5807.4  5811.1 

157 

5814.8  5818.5  5822.2 

5825-9 

5829.6 

5833.3  5837.   5840.7 

5844.4  |  5848.1 

158 

5851.9  5855.6  5859.3 

5863. 

5866.7 

5870.4  5874.1 

5877.8 

!  5881.5  i  5885.2 

159 

5888.9 

5892.6  5896-3 

5900. 

5903.7 

5907.4  59H-I 

5914.8 

5918.5 

5922.2 

1  60 

5925.9 

5929.6  5933-3 

5937- 

5940.7 

5944.4  5948.1  5951.9 

I  5955-6 

5959-3 

161 

5963. 

5966.7 

5970.4 

5974-1 

5977-8 

5981.5 

5985.2 

5988.9 

5992.6 

5996.3 

162 

6000. 

6003.7 

6007.4 

6011.1 

6014.8  6018.5 

6022.2  6025.9 

1  6029.6 

6033.3 

163 

6037. 

6040.7 

6044.4 

6048.1 

6051.9 

6055.6 

6059.3 

Cc63. 

6066.7 

6070.4 

164 

6074.1 

6077-8 

6081.5 

6085.2 

6088.9  !  6092.6 

6096.3 

6100. 

1  6103.7 

6107.4 

165 

6111.1 

6114.8 

6118.5 

6122.2  6125.9  6129.6 

6133-3 

6137. 

I  6140.7 

6144.4 

166 

6148.1 

6151.9 

6155-6 

6159.3  6163.   6166.7 

6170.4 

6174.1 

!  6177.8 

6181.5 

167 

6185.2 

6188.9 

6192.6 

6196.3 

6200.  6203.7 

6207.4 

6211.1 

!  6214.8 

6218.5  l 

168 

6222.2 

6225.9 

6229.6 

6233.3 

6237.  6240.7 

6244.4 

6248.1 

6251.9 

62-55.6 

169 

6259.3 

6263. 

6266.7 

6270.4 

6274.1 

6277.8 

6281.5 

6285.2 

6288.9 

6292.6 

170 

6296.3 

6300. 

6303.7 

6307.4 

6311.1  6314.8 

6318.5 

6322.2 

1  6325.9 

6329.6 

6333.3 

6337. 

6340.7 

63444 

6348.1  6351.9 

6355.6 

6359-3 

6363. 

6366.7 

172 

6370.4 

6374.1 

6377.8 

6381.5 

6385.2  6388.9 

6392.6 

6396-3 

|  6400. 

6403.7 

173 

6407.4 

6411.1 

6414.8 

6418.5  6422.2  6425.9 

6429.6 

!  6437- 

6440.7 

174 

6444.4 

6448.1 

6451.9 

6455.6  6459.3  I  6463. 

6466.7 

6470.4 

6474.1 

6477.8 

175 

6481.5 

6485.2 

6488.9 

6492.6  6496.3  |  6500. 

6503-7 

6507.4 

6511.1 

6514-8 

176 

6518.5 

6522.2 

6525-9 

6529.6  6533.3  6537. 

6540.7 

6544.4 

6^48  1 

655L9 

177 

6555.6 

6559-3 

6563- 

6566.7  6570.4  6574.1  6577.8 

6581.5 

6585.2 

6588.9 

178 

6592.6 

6596-3 

6600. 

6603.7  6607.4  6611.1 

6614.8  6618.5 

6622.2 

6625.9 

179 

6629.6 

6633.3 

6637. 

6640.7 

6644.4  6648.1  6651.9  6655.6 

6659.3  6663. 

180 

6666.7 

6670.4 

6674.1 

6677.8 

6681.5 

6685.2  |  6688.9  6692.6 

6696.3 

6700. 

181 

6703.7 

6707.4 

6711.1 

6714.8 

6718.5  6722.2 

6725.9 

6729.6 

6733-3 

6737. 

182 

6740.7 

6744.4 

6748.1 

6751-9 

6755-6  6759.3 

6763. 

6766.7 

6770.4 

6774.1 

183 

6777.8 

6781.5 

6785.2 

6788.9 

6792.6  6796.3 

6800. 

6803.7 

6807.4 

6811.1  i 

184 

6814.8 

6818.5 

6822.2 

6825.9 

6829.6  6833.3  6837. 

6840.7 

6844.4 

6848.1  i 

185 

6851.9 

6855.6 

6859-3 

6863. 

6866.7  6870.4 

6874.1 

6877.8 

6881.5 

6885.2 

186 

6888.9 

6892.6 

6896.3 

6900. 

6903.7  i  6907.4 

6911.1 

6914.8 

6918.5 

6922.2   ! 

187 

6925.9 

6929.6 

6933.3 

6937. 

6940.7  6944.4 

6948.1  6951.9 

6955-6 

6959.3 

188 

6963. 

6966.7 

6970.4 

6974.1 

6977.8  6981.5  6985.2  6988.9 

6992.6 

6996.3 

189 

7000. 

7003.7  7007.4 

7011.1  7014.8  7018.5  7022.2  7025.9 

7029.6 

7033-3 

190 

7037. 

7040.7  7044.4 

7048.1  7051-9  i  7055-6  7059-3 

7063. 

7066.7 

7070.4 

191 

7074.1 

7077.8  7081.5 

7085.2  7088.9  7092.6  1  7096.3  7100. 

7103.7 

71074 

192 

7111.1 

7114.8  7118.5 

7122.2  7125.9:  7129.6!  7133.3  7137. 

7140.7 

71444   , 

193 

7148.1 

7I5I-9  17155-6  7i593l7i63.  17166.717170.4  71741 

7177-8 

7I8I.5 

194 

7185.2 

7188.9  1  7192.6 

7196.3  7200.  |  7203.7  7207.4  7211.1 

72148  7218.5  1 

195 

7222.2 

7225.9  7229.6 

7233-3  7237.   7240.7  72444  7248-1 

7251-9 

7255.6 

196 

7259.3 

7263. 

7266.7 

7270.4 

7274.1 

7277.8  7281.5  7285.2 

7288.9  72926 

197 

7296.3 

7300. 

73037 

73074 

7311.1 

7314.8  7318.5  7322.2 

73259 

7329.6 

jig8 

7333-3 

7337- 

7340.7 

7344-4 

7348.1 

7351-9  7355-6 

7359-3 

7363. 

7366.7 

199 

7370.4 

7374-1 

7377-8 

7381.5 

7385-2 

7388.9 

7392-6 

7396.3 

7400. 

7403  7 

200 

7407.4 

7411-1 

7414.8 

7418.5 

7422.2 

7429.6 

7433-3 

7437- 

7440.7 

o. 

I.       2. 

3- 

4- 

5- 

6. 

7- 

8. 

9 

i               i 

• 

52 
TABLE  Xo.   4— CONTINUED. 


;  Areas . . . .  j  o.i 


I  o.i  j  0.2     0.25  j  0.3     0.410.5     0.6     0.7     0.75     0.8     0.9 


Contents.  ...  .........  |  0.4  1  0.7 


n 


-1.5     1.9 


2.6 


Areas  :  Tens  in  left  Column  and  Units  at  top.     Contents  for  IQQfcci 
in  cubic  yards  in  body  of  Table. 


4> 

9 

PEI 

0.   |    , 

2. 

3- 

4- 

5. 

6. 

tj  ^ 

8. 

i 
9- 

2DI 

7444.4 

7448.1 

745I.9|  7455.6 

7459-3 

7463. 

7466.7  7470.4 

7474-1 

7477-8 

202 

7481.5 

7485-2 

7488.9  '  7492.6 

7496.3 

7500. 

7503-7 

75074 

75H.I 

7514-8 

2^3  1  75IS.5 

7522.2 

7525-9  7529.6 

7533-3 

7537- 

7540-7 

7544-4 

7548.1 

7551-9 

204 

7555-6 

7559-3 

7563.   7566.7 

7570.4 

7574-1 

7577-8 

7581.5 

7585.2 

7588.9 

205 

7592.6 

7596-3 

7600. 

7603.7 

7607.4 

7611.1 

7614.8 

7618.5 

7622.2 

7625.9 

206 

7629.6 

7633-3 

7637. 

7640.7 

7644.4 

7648.1 

7651.9 

7655.6  7659.3 

7663. 

207 

7666.7 

7670.4 

7674.1 

7677.8 

7681.5 

7685.2 

7688.9 

7692.6 

7696.3 

7700. 

208 

7703.7 

7707-4 

77II.1 

7714.8  7718.5 

7722.2 

7725.9  7729.6 

7733-3 

7737- 

209 

7740.7 

7744-4 

7748.1 

7751-9  7755-6 

7759-3 

7763.  !7766.7 

7770.4 

7774-1 

210 

7777-8 

778i.5 

7785-2 

7788.9  1  7792.6 

7796.3 

7800. 

7803.7 

7807.4 

7811.1 

211 

7814.8 

7818.5 

7822.2 

7825.9  j  7829.6 

7833.3 

7837. 

7840.7 

7844.4 

7848.1 

212 

7851.9 

7855.6 

7859-3  7863.  !  7866.7 

7870.4 

7874.1 

7877.8 

7881.5 

7885.2 

2I3 

7888.9 

7892.6 

7896.3  7900. 

7903.7 

79074 

7911.1 

7914.8 

7918.5 

7922.2 

2I4 

7925.9 

7929.6 

7933-3  !  7937- 

7940.7 

7944-4 

7948.1 

7951-9 

7955-6 

7959-3 

215 

7963- 

7966.7 

7970.4  7974-1 

7977-8 

798i.5 

7985.2 

7988.9 

7992.6 

7996.3 

216 

8000. 

8003.7 

8007.4 

8011.  i 

8014.8 

8018.5 

8022.2 

8025.9 

8029.6 

8033-3 

217 

8037. 

8040.7 

8044.4 

8048.1 

8051.9 

8055.6 

8059.3 

8063. 

8066.7 

8070.4 

2x8 

8074.1 

8077.8 

8081.5  8085.2  8088.9 

8092.0 

8096.3 

8100. 

8103.7 

8107.4 

219 

8111.1 

8114.8 

8118.5  8122.2  8125.9 

8129.0 

0133-3 

8i37. 

8140.7 

8144.4 

220  8148.1 

8151.9  8155.6 

8159.31  8163. 

8166.7 

8170.4 

8174.1 

8177-8 

8181.5 

221  8185.2 

8188.9  8192.6 

8196.3  8200. 

8203.7 

8207.4 

8211.1 

8214.8 

8218.5 

222  8222.2 

8225.9 

8229.6 

8233-3 

8237. 

8240.7 

8244.4 

8248.1 

8251.9 

8255-6 

223  8259.3 

8263. 

8266.7 

8270.4  8274.1 

8277.8 

8281.5 

8285.2 

8288.9 

8292.6 

224  8296.3 

8300. 

8303.7  8307.4  8311.1 

8314-8 

8318.5 

8322.2 

8325.9!  8329.6 

225  8333.3 

8337. 

8340.7  8344.4  8348.1 

8351-9 

8355-6 

8359.3 

8363- 

8366.7 

226  8370.4 

8374.1 

8377.8 

8381.5  8385.2 

8388.9 

8392.6 

8396.3 

8400. 

8403-7 

227  8407.4 

8411.1 

8414.8  8418.5  j  8422.2 

8425.9 

8429.6 

8433.3 

8437. 

8440.7 

228  !  8444.4 

8448.1  8451.9  8455.6  8459.3 

8463. 

8466.7 

8470.4  8474.1 

8477-8 

229  8481.5 

8485.2 

8488.9 

8492.6  i  8496.3 

8500. 

8503-7 

8507.4  8511.1 

8514-8 

230  8518.5 

8522.2 

8525-9 

8529.6!  8533.3 

8537. 

8540.7 

8544.4  8548.1 

855L9 

23r 

8555-6 

8559-3J  8563. 

8566.7 

8570.4 

8574.1 

8577.8 

8581.5 

8585-2 

8588.9 

232  1  8592.6 

8596.3  8600. 

8603.7 

8607.4 

8611.1 

8614.8 

8618.5 

8622.2 

8625.9 

233  i  8620.6 

8633.3  I  8637. 

8640.7 

8644.4 

8648.1 

8651.9 

8655.6 

8659-3 

8663. 

234 

8666.7 

8670.4 

8674.1 

8677.8 

8681.5 

8685.2 

8688.9 

8692.6 

8696.3 

8700. 

235 

8703.7 

8/07.4 

8711.1  8714.8  8718.5 

8722.2 

8725-9 

8729.6 

8733-3 

8737. 

O  J 

236 

8740.7 

8744.4 

8748.1  8751.9  8755.6 

8759-3 

8763. 

8766.7 

8770.4  8774.1 

237 

8777.8 

8781.5 

8785.2  8788.9 

8792.6 

8796.3 

8800. 

8803.7 

8807.4  8811.1 

238 

8814.8 

8818.5 

8822.2  8825.9 

8829.6 

8833-3 

8837. 

8840.7 

8844.4  8848.1 

239 

8851.9 

8855-6 

8859-3 

8863.   8866.7 

8870.4 

8874.1 

8877.8 

8881.5  8885.2 

240 

88880 

8892.6 

8896.3 

8900. 

8903.7 

8907.4 

8911.1 

8914.8 

8918.5  8922.2 

241  8925.9 

8929.6 

8933-3 

8937. 

8940.7 

8944.4 

8948.1 

8951.9 

8955-618959.3 

242  8963. 

8966.7 

8970.4  8974.1  8977.8 

8981.5 

8985.2 

8988.9 

8992.6  ;  8996.3 

243 

9000. 

9003.7 

9007.4  9011.1  9014.8 

9018.5 

9022.2 

9025.9 

9029.6  i  9033.3 

244  9037. 

9040.7 

9044.4 

9048.1 

9051.9  9055.6 

9059-3 

9063. 

9066.7  :  9070.4 

245  9074.1 

9077.8 

9081.5  9085.2 

9088.9 

9092.6 

9096.3 

9100. 

9103.7 

9107.4 

246  9111.1 

9114.8  19118.5  j  9122.2  9125.9 

9129.6 

9r33-3 

9!37- 

9140.7 

9144.4 

247  9148.1 

9T5i9 

9I55-6  !  9*59-3  9l63- 

9166.7 

9170.4 

9174.1 

9177.8  9181.5 

248!  9185.2 

9188.9 

9192.6  i  9196.3  i  9200. 

9203.7 

9207.4 

9211.1 

9214.8 

9218.5 

249  Q222.2 

9225.9  |  9229.6  9233.3  9237. 

9240.7 

9244.4 

9248.1 

9251.9 

9255-6 

250 

9259-3 

9263.  9266.7 

9270.4  9274.1 

9277.8 

9281.5  9285.2  9288.9 

9292.6 

o.  j   i.     ».     3-     4-     5- 

6.     7- 

8. 

9- 

1      i                • 

1 

53 
TABLE  No.  4— CONTINUED. 


j  Areas  .... 

O.I  I    O.2 

0.25 

CM 

0.4  1  0.5 

06 

O.y 

O.7<i 

0.8  i  o.q  ' 
" 

(Contents.  .  .  

0.4  1  0.7 

0.9 

i.i 

1.5  1  1.9 

2.2 

2.6 

2.8 

3-0  1  3-3 

Areas:  Tens  in  left  Column  and  Units  at  top.     Contents  for  IQQfeet 
in  cubic  yards  in  body  of  Table. 


o  ! 

£   o. 

I. 

2. 

3- 

4- 

5-     6. 

7- 

8. 

9- 

251 

9296.3 

9300. 

9303.7  9307.4 

9311.1  9314-8;  93I8.5J  9322.2  9325.9 

9329.6 

252 

9333-3 

9337- 

9340.7  9344-4 

9348.1!  9351.9  9355.6  9359.3  9363. 

9366.7 

253 

9370.4  9374-1 

9377-8  9381.5 

9385.2'  9388.9!  9392.6  9396.3  9400. 

9403.7 

254 

9407.4  9411.1 

9414.8  9418.5!  9422.2  9425.9!  9429.6  9433.3 

9437- 

9440.7 

255 

9444-4 

9448.1 

9451.9;  9455-6 

9459.3  9463. 

94667 

9470.4 

9474.1 

9477.8 

256 

9481.5 

9485.2 

9488.9!  9492-6!  9496.3 

9500. 

9503-7  9507-4 

9511.1 

9514.8 

257 

9518.5 

9522.2 

9525.9 

9529.6  9533.3 

9537- 

9540-71  9544-4 

9548.1 

9551-9 

258 

9555-6 

9559-3 

9563. 

9566.7 

9570.4 

9574-ii  9577-8  9581.5 

9585.2 

9588.9 

259 

9592.6 

9596.3  9600. 

9603.7 

9607.4 

9611.1 

9614.8  9618.5  9622.2 

9625.9 

260 

9629.6 

9633-3  9637. 

9640.7 

9644.4 

9648.1 

9651.9  9655.6 

9659-3 

9663. 

261 

9666.7 

9670.4  9674.1 

9677.8 

9681.5 

9685.2 

9688.9)  9692.6 

9696.3 

9700. 

262 

9703.7 

9707.4  9711.1 

9714.8 

9718.5 

9722.2 

9725.9  9729-6 

9733-3 

9737- 

263 

9740.7 

9744-4 

9748.1 

975T-9 

9755-6 

97593 

9763. 

9766.7 

9770.4 

9774-1 

264 

9777-8 

9781.5 

9785.2 

9788.9 

9792.6 

9796.3  9800. 

9803.7 

9807.4!  9811.1 

265 

9814.8 

9818.5 

9822.2 

9825.9 

9829.6 

9833-3  9837. 

9840.7 

9844.4 

9848.1 

266 

9851.9 

9855.6 

9859-3 

9863. 

9866.7  9870.4  9874.1  9877.8 

9881.5 

9885.2 

267 

9888.9 

9892.6 

9896.3 

9900. 

9903.7  9907.4  9911.1  9914.8  9918.5!  9922.2 

268 

9925-9 

9929.6 

9933-3 

9937- 

9940.7 

9944.4)  9948.1 

9951.9]  9955.6 

9959-3 

269 

9963. 

9966.7 

9970.4 

9974-1 

9977.SJ  9981.5)  9985.2  9988.9  9992.6 

9996.3 

270 
271 

1  0000. 

10037. 

10003.7  10007.4 
10040.7110044.4 

IOOII.I 

10048.1 

IOOI4.8!  IOOl8.  5IIOO22.  2  10025.9 
I005I.9  10055.6  10059.3^0063. 

10029.  6'  10033.  3 
10066.7  10070.4 

272 

10074.1  10077.8  10081.5 

10085.2 

10088.9:  10092.6!  10096.3!  10100. 

10103.7 

10107.4 

273 

101  1  1.  1  110114.8  10118.5 

IOI22.2 

10125.9  10129.6  10133.3  10137. 

10140.7 

10144.4 

274 

10148.1  10151.9  10155.6 

IOI59.3 

10163. 

10166.7  10170.4  10174.1  10177.8 

10181.5 

275 

10185.2  10188.9110192.6 

10196.3 

IO2OO. 

10203.7  102074!  I02II.I  I02I4.8!  I02I8.5 

276 

10222.2)10225.9 

10229.6 

10233.3 

10237. 

10240.7  10244.4  IO248.I  10251.9 

10255.6 

277 

10259.3  10263. 

10266.7 

10270.4 

I0274.I  10277.8  I028I.5 

10285.2110288.9 

10292.6 

278 

10296.3  10300. 

10303.7 

10307.4 

I03II.I  10314.8  I03I8.5 

10322.2 

10325.9110329.6 

279 

I0333-3jio337. 

10340.7  10344.4 

I0348.I  I035I.9  10355.6110359.3  10363. 

10366.7 

280 

10370.410374.1 

10377.8  10381.5 

10385.2  10388.9  10392.6!  10396.3!  IO4OO. 

10403.7 

281 

10407.4  10411.1 

10414.8 

10418.5 

10422.2  10425.9  10429.6  10433.3  10437. 

10440.7 

282 

10444.410448.1 

10451.9 

10455.6 

10459.3  10463. 

10466.7  10470.4  10474.1 

10477.8 

283 

10481.  5  [10485.  2 

10488.9  10492.6  10496.3  10500. 

10503.7  10507.4  10511.1 

10514.8 

284 

10518.5  10522.2 

10525.9 

10529.6 

10533.3  I0537- 

10540.7  10544.4  10548.1 

10551-9 

285 

10555.6  10559.3 

10563. 

10566.7  10570.4  10574.1 

10577.8  10581.5  10585.2 

10588.9 

286 

10592.6 

10596.3 

10600. 

10603.7 

10607.4!  10611.  1  110614.8 

10618.5  10622.2  10625.9 

287 

10629.6 

10633.3 

10637. 

10640.7 

10644.4  10648.1  10651.9 

10655.6  10659.3110663. 

288 

10666.7 

10670.4 

10674.1 

10677.8 

I068l.  5^10685.  2  10688.9 

10692.6  10696.3 

10700. 

289 

10703.7 

10707.4 

10711.1 

10714.8  I07I8.5 

I0722.2!I0725.9 

10729.6  10733.3 

10737. 

290 

10740.7 

10744.4110748.1 

I075I.9 

10755-6 

10759.3  10763. 

10766.7  10770.4 

10774.1 

291 

10777.8 

10781.5  10785.2  10788.9 

10792.6  10796.3  10800. 

10803.7  10807.4  10811.  i 

292 

10814.8 

10818.5 

10822.2110825.9!  10829.6  10833.3110837. 

10840.7  10844.4 

10848.1 

2Q3 

10851.9  10855.6  10859.3  10863. 

10866.7  10870.4:10874.! 

10877.8  10881.5  10885.2 

294 
295 

10888.9  10892.6  10896.3  10900. 
10925.9  10929.6!  10933.3110937. 

10903.7 
10940.7 

I09074JI09II.I  10914.8110918.5 
I09444JI0948.I  10951.9'  10955.6 

10922.2 
10959-3 

296 

10963. 

10966.7  10970.4110974.1110977.8  10981.5 

10985.  2110988.9  10992.6 

10996.3 

297  nooo. 

11003.7  11007.4  noii.  i  11014.8  11018.5 

1  1022.2]  1  1025.9!  1  1029.6!  1  1033.  3 

298 

11037. 

1  1040.7!  1  1044.4  !  1048.1  1  105  i.g'  1  1055.6 

11059.3  11063. 

11066.7 

11070.4 

299 

11074.1  11077.8  11081.5  11085.2 

HO88.9jIIO92.6 

11096.3 

moo. 

11103.7 

11107.4 

300 

IIIII.IjIIII4.8  IIII8.5  IH22.2 

III25.9  III29.6 

III33-3 

11137. 

11140.7 

11144.4 

0.       I.      2. 

3- 

<• 

5. 

6. 

— 
7.    8. 

g. 

54 
TABLE  Xo.  4— CONTINUED. 


Areas  

O  I 

O  2 

O  2$ 

O  ^ 

04. 

o  5 

o  6 

O  7 

O  7^ 

08 

o  9  i 

[Contents  

0.4 

0.7 

0.9 

I.I 

15 

1.9 

2  2 

2.6 

2.8 

30 

J 

.4  raw  ;  Tens  in  left  Column  and  Units  at  top.      Contents  for  IQQfeet 
in  cubic  yards  in  body  of  Table. 


1  -si 

1 

o. 

I- 

2.     3.     4- 

5- 

6. 

• 

7- 

8. 

9. 

1301 

11148.1 

III5I.9 

11155.6  11159.3  11163. 

11166.7 

11170.4 

11174.1  11177.8  11181.5 

302 

11185.2 

IllSS.g 

11192.6  11196.3  1  1  200. 

11203.7 

11207.4 

II2II.I  II2I4.8  II2I8.5 

303 

II222.2 

II225.9 

11229.6,11233.3  11237. 

11240.7 

11244.4 

II248.I  11251.9:11255.6 

1304 

11259.3 

II263. 

11266.7  1  1  270.4;  1  1274.  i 

11277.8 

11281.5 

II285.2  11288.9:11292.6 

305 

11296.3 

II3OO. 

11303.7  11307.411311.1 

11314.8 

11318.5 

II322.2  11325.9  11329.6 

306 

II333-3 

II337- 

11340.7  11344.4:11348.1 

11351.9 

II355-6 

II359.3  H363. 

11366.7 

307 

11370.411374.! 

11377.8  11381.5111385.2  11388.9 

11392.6 

11396.3  II400. 

11403.7 

5308 

11407.4 

II4II.I 

11414.8  11418.5  11422.2  11425.9 

11429.6 

II433.3  II437- 

11440.7 

309 

II4444 

II448.I 

11451.9  11455.6  11459.3  11463. 

11466.7 

II470.4  H474.I 

11477.8 

310 

11481.5 

11485.2 

11488.9  11492.6:11496.3  11500. 

11503-7 

11507.4111511.1 

11514.8 

311 

II5I8.5 

II522.2 

11525.911529.611533.311537. 

11540.7 

II5444 

H548.I 

"551.9 

312 

II555-6 

1*559-3 

11563. 

II566.7  II570.4  II574-I 

II577-8 

H58I.5 

11585-2 

11588.9 

313 

II592.6  11596.3 

11600. 

11603.7  Ii6o7.4!ii6ii.i 

11614.8 

Il6l8.5 

11622.2 

11625.9 

i3i5 

11629.6 
II666.7 

11633.3  11637. 
11670.4  11674.1 

11640.7  11644.4  11648.1 
11677.8  11681.5  11685.2 

11651.9 
11688.9 

11655.6 
11692.6 

11659.3  11663.' 
11696.3  11700. 

316 

II703.7 

11707.4 

11711.1 

11714.8  11718.5  11722.2 

11725.9 

11729.6 

Ii733.3;ii737. 

317 

II740.7 

11744.4 

11748.1 

11751.9  II755-6  H759-3 

11763. 

II766.7 

11770.4  11774-1 

II777.8 

11781.5 

11785.2 

11788.9  11792.6  11796.3  11800. 

11803.7 

11807.4  uSii.i 

319 

11814.8 

11818.5 

11822.2 

11825.9111829.6  11833.3 

11837- 

11840.7 

11844.4  11848.1 

320 

11851.9 

11855.6 

11859.3  11863.  11866.7  11870.4 

11874.1 

II877.8 

11881.5  11885.2 

321 

II888.9 

11892.6 

11896.311900.  11903.711907.4 

11911.1 

11914.8 

11918.5  11922.2 

322 

11925.9 

11929.6 

H933.3 

11937.  11940.7:11944.4 

11948.1 

II95I.9 

11955.611959-3 

323 

11963. 

11966.7 

11970.4  11974.1  11977-8  11981.5 

11985.2 

11988.9 

11992.611996.3 

324 

I2OOO. 

12003.7 

120074  I20II.I  I20I4.8 

12018.5 

12022.2 

12025.9 

12029.6  12033.3 

325 

12037. 

12040.7 

12044.4  I2O48.I  12051.9 

12055.6 

12059.3 

12063. 

12066.7  12070.4 

326 

I2O74.I 

12077.8 

I208I.5 

12085.2  12088.9  12092.6 

12096.3 

I2IOO. 

12103.7  12107.4 

327 

I2III.I 

I2II8.5 

I2I22.2  12125.9  I2I29.6 

I2I33-3 

I2I37.0 

12140.7  12144.4 

328 

I2I48.I 

12151.9 

I2I55.6  12159.3  12163. 

12166.7 

I2I70.4 

I2I74.I 

12177.8  12181.5 

329 

I2I85.2 

12188.9 

I2I92.6  12196.3  12200. 

12203.7 

122074 

I22II.I 

12214.8  12218.5 

330 

12222.2 

12225.9 

12229.6 

12233.3  12237. 

12240.7 

12244.4 

I2248.I  12251.9  12255.6 

331 

12259.3 

12263. 

12266.7 

I227O.4  I2274.I  12277.8 

I228I.5 

12285.2 

12288.9  12292.6 

332 

12296.3 

12300. 

12303.7 

12307.4  I23II.I  I23I4.8 

I23I8.5 

12322.2 

12325.9  12329.6 

333 

12333-3 

12337. 

12340.7 

12344.4  I2348.I 

12351-9 

12355-6 

12359-3 

12363. 

12366.7 

334 

12370.4 

12374.1 

12377.8 

12381.5112385.2 

12388.9 

12392.6 

12396.3 

12400. 

12403.7 

335 

12407.4 

12411.1 

I24I4.8 

12418.5  12422.2 

12425.9 

12429.6 

12433-3 

12437. 

12440.7 

336 

12444.4 

12448.1 

12451.9 

12455.6  12459.3112463. 

12466.7 

12470.4 

12474.1 

12477.8 

337 
338 

12481.5 
I25I8.5 

12485.2 
12522.2 

12488.9  12492.6  12496.3'  I25OO. 
12525.9  12529.6  12533.3  12537. 

12503.7 
12540.7 

12507.4 
12544.4 

12511.1 

12548.1 

12514.8 
12551-9 

339 
340 

12555-6 
12592.6 

12559-3 
12596.3 

12563. 
12600. 

12566.7  12570.4  I2574.I 
12603.7  12607.4  126II.I 

12577-8 
12614.8 

12581.5 
I26I8.5 

12585.2 
12622.2 

12588.9 
12625.9 

12629.6 

12633.3 

12637. 

12640.7  12644.4 

12648.1 

12651.9 

12655.6 

12659.3 

12663. 

342 

12666.7 

12670.4 

I2674.I 

12677.8  12681.5 

12685.2 

12688.9 

12692.6 

12696.3 

12700. 

343 

12703.7 

12707.4 

I27II.I 

12714.8  I27I8.5 

12722.2 

12725.9 

12729.6  12733.3 

12737. 

344 

12740.7 

12744.4 

I2748.I 

I275I.9  12755.6 

12759.3 

12763. 

12766.7  12770.4 

12774.1 

345 

12777.8 

12781.5 

12785.2  12788.9  12792.6 

12796.3 

12800. 

12803.7  12807.4112811.1 

346 

I28I4.8 

12818.5 

12822.2  12825.9  12829.6 

12833.3 

12837. 

12840.7 

12844.4  12848.1 

347 

12851.9 

12855.6 

12859.3 

12863.  12866.7 

12870.4 

I2874.I 

12877.8 

12881.5  12885.2 

348 

12888.9 

12892.6 

12896.3 

I29OO.  12903.7 

12907.4  12911.1 

12914.8  I29l8.5|l2922.2 

349 

12925.9 

12929.6 

12933-3 

12937.  12940.7 

12914.4 

12948.1 

12951.9 

12955-6 

12959-3 

35<> 

12963. 

12966.7 

12970.4  12974.1  12977.8  12981.5  12985.2 

12988.9  12992.6  12996.3 

0. 

i. 

2.       3.       4. 

5- 

£ 

7- 

8. 

9- 

. 

55 
TABLE  So.  4— CONCLUDED. 


(Areas   »                                1  o  I  1  o  2 

O  2Z 

o  3 

O  4 

o  5 

06 

O  7  1    O  7^ 

08 

o  9 

IContents  I  0.4  1  0.7 

09 

i.i 

i-5 

1.9 

2.2 

2.6  1    2.8 

3-0 

3-3 

Areas;  Tens  in  left  Column  and  Units  at  top.     Contents  for  IQQfeet 
in  cubic  yards  in  body  of  Table. 


1 

o. 

i. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9- 

35i 

13000. 

13003.7 

13007.4  I3OII.I  13014.8 

I3OI8.5  I3O22.2 

13025.9 

13029.6 

13033-3 

352 

13037- 

13040.7 

13044.4  13048.1113051.9 

I3055-6 

13059.3 

13063.  13066.7 

13070.4 

353 

13074.1 

13077.8  13081.5  13085.2 

13088.9 

13092.6  13096.3 

13100. 

13103-7 

13107.4 

354 
355 

13111.1113114.8  13118.5  13122.2 
13148.1  13151.9  13155.6  I3I59-3 

13125-9 
13163- 

13129.6113133.3 
13166.7113170.4 

I3I37. 
I3I74-I 

13140.7 
13177.8 

13144.4 
13181.5 

356 

13185.2  13188.9  13192.6  13196.3 

13200. 

13203.7 

13207.4113211.1 

13214.8 

13218.5 

357 

13222.2  13225.9 

13229.613233.3:13237. 

13240.7  132444 

13248.1 

13251.9 

13255-6 

358 

13259.3  13263. 

13266.7  13270.4 

13274.1 

13277.8  I328I.5 

13285.2 

13288.9 

13292.6 

359 

13296.3  13300. 

I33°3-7|I33O74  \I3311-1  *33  1.4-8  j  1331  8.  5 

13322.2 

133259 

13329-6 

36o 

13333-3  13337- 

13340.7  13344-4 

I3348.I 

!335i-9  !3355-6 

13359-3 

13363. 

13366.7 

13370.4  I3374-I 

13377-8 

I338I.5! 

13385-2 

13388.9  13392-6 

13396-3 

13400. 

I3403-7 

362 

13407.413411.1 

13414.8 

13418.5; 

13422.2 

13425-9 

13429.6 

13433-3 

13437- 

13440.7 

363 

134444 

13448.1 

I345L9 

I3455-6: 

13459-3 

13463- 

13466.7113470.4 

13474.1113477.8 

364 

13481.5113485.2 

13488.9 

13492.6 

13496.3 

13500. 

13503.7 

I3507-4 

I35H.I 

I35I4.8 

365 

13518.5 

13522.2 

13525.9 

13529.6 

13533-3 

13537. 

135407 

13544-4 

13548.1113551.9 

366 

13555-6 

13559-3 

13563- 

13566.7 

13570.4  I3574.I 

13577.8 

13581.5 

13585-2 

13588.9 

367 

13592.6 

13596.3 

13600. 

13603.7113607.4 

13611.1  13614.8 

13618.5 

13622.2 

13625.9 

368 

13629.6 

13633-3 

13637- 

13640.7 

13644.4  13648.1 

13651.9113655.6 

13659-3 

13663. 

369 

13666.7 

13670.4 

13674.1 

13677-8 

13681.5113685.2 

13688.9 

13692.6 

13696.3 

13700. 

370 

13703-7 

137074 

13711.1 

13714-8 

13718.5  13722.2 

13725.9 

13729.6  13733.3 

13737- 

371 

13740.7 

137444 

13748.1 

I375L9 

I3755.6JI3759-3I3763. 

13766.7 

13770.4 

I3774-I 

372 

13777-8 

13781.5 

13785-2  13788.9 

13792.6113796.3  13800. 

13803  7 

13807.4 

13811.1 

373 

13814.8 

13818.5 

13822.2  13825.9 

13829.6 

13833.3 

13837. 

13840.7113844.4 

13848.1 

374  13851-9 
375  113888.9 

13855.6113859.3  13863.  1  13866.7  13870.4  13874.1 
13892.6113896.3  13900-  13903-7  139074  I39H.  ! 

13877.8 
13914.8 

13881.5 
I39I8.5 

13885.2 
.13922.2 

376  13925-9 

13929.6  13933.3 

13937-  13940.7 

13944-4 

I3948.I 

I395L9 

13955-6 

13959-3 

377  13963- 

13966.7  13970.4 

I3974.i|i3977.8 

13981-5 

13985-2 

13988.9 

13992.6 

13996.3 

378  14000. 

14003.7 

14007.4  14011.1 

14014.8114018.5 

14022.2 

14025.9 

14029.6  14033.3 

379  !  14037. 

14040.7 

14044.4  14048.1  14051.9 

14055.6 

14059-3 

14063. 

14066.7 

14070.4 

380  14074.1 

14077.8 

14081.5 

14085.2 

14088.9 

14092.6 

14096.3 

14100. 

14103.7 

;  14107.4, 

381  14111.1 

14114.8 

14118.5 

14122.2 

14125.9 

14129.6 

I4I33.3 

14137.4114140.7  14144-4 

382  114148.1 

14151.9 

I4I55.6 

I4I59.3 

14163- 

14166.7 

14170.4 

14174.1 

14177.8 

14181.5 

383  14185-2 

14188.9 

14192.6 

14196.3 

14200. 

14203.714207.4114211.1 

14214.8 

;i42i8.5 

384114222.2 
385  1,14259-3 
386  114296.3 

14225.9 
14263. 
14300. 

14229.6 
14266.7 
14303-7 

14233.3  14237. 
14270.4  14274.1 
14307.414311.1 

14240.7 

14277-8 
I43I4.8 

14244.4  14248.1,14251.9  14255.6 
14281.5  14285.2  14288.9  14292.6 
14318.5  14322.2!  14325.9^14329.6 

387 

14333.3 

14337- 

14340.7  143444 

14348.1 

I435I-9 

14355-6 

14359.3 

14363. 

14366.7 

388 

14370.4 

I4374-I 

14377.8  14381.5 

14385-2 

14388.9 

14392.6  14396.3 

14400. 

114403.7 

389 

14407.4 

14411.1  14414.8  14418.5 

14422.2 

14425.9 

14429.6114433-3 

I4437- 

14440.7 

390 

14444.4 

14448.1  14451-9 

14455.6114459.3 

14463. 

14466.7 

14470.4 

14474.1 

14477.8 

14481.5 

14485.2  14488.9  14492  6 

14496.3 

14500. 

14503.7 

14507.4 

I45H.I 

14514-8 

392 
393 

14518.5 
14555-6 

14522.2  14525-9 
14559.3  14563. 

14529.614533.314537. 
14566.7114570.4  14574.1 

14540.7 

14577.8 

14544-4 
14581.5 

I4548.J 
14585-2 

I455L9 

14588.9 

394 

14592-6 

14596.3  14600. 

14603.7 

14607.4 

14611.1 

14614.8 

14618.5 

14622.2  14625.9 

395  114629.6 
396114666.7 

14633.3  14637- 
14670.4  14674.1 

14640.7  146444  14648-1 
14677.8;  14681.5]  14685.2 

14651.9  14655.6 
14688.9  14692.6 

14659-3 
14696-3 

!  14663. 
14700. 

397  14703-7  147074  I47II-I 

14714.8 

14718.5 

14722.2  14725-9 

14729.6 

14733.3 

:  14737. 

398114740.7 

14744.4 

14748.1 

I475L9 

14755-6 

14759-3 

14763. 

14766.7 

14770.4 

14774.1 

399IM777-8 

14781.5 

14785.2 

14788.9 

14792.6 

14796.3 

14800. 

14803.7 

14807.4 

14811.1 

400  14814.8 

14818.5 

14822.2  14825.9 

14829.6 

14833.3 

14837. 

14840.7 

14844.4 

14848.1 

1  * 

i. 

2. 

3- 

4- 

5. 

6, 

7- 

8. 

9. 

56 

TABLE  Ko.  5. 

Minus  Corrections  corresponding  to  N~~N',  or  n~n',  and  general  for 
all  side  slopes.     For  computation  by  average  Areas. 

Difference  of  Correction  numbers  in  feet  and  tenths  in  left  column  and 
at  top  ;   Correction  in  cubic  yards  for  100  ft.  in  body  of  Table. 


!     *J     , 

i 

V 

£ 

0. 

i. 

2. 

3- 

4- 

5- 

6. 

7- 

8. 

9- 

o 

0.0             0.0 

00 

O.I 

O.I             0.2 

0.2 

0-3 

0.4 

0-5 

i 

0.6 

0.7 

0.9 

I.O 

1.2 

1.4 

1.6 

1.8 

2.0 

2.2 

2 

2-5 

2-7 

3-0 

3-3 

3-6 

3-9 

4-2 

4-5 

4.8 

5-2 

3 

5-6 

5-9 

6-3 

6-7 

7.1 

7-6 

8.0 

8-5 

8.9 

94 

4 

99 

10.4 

10.9 

11.4 

12.0 

12.5 

13.1 

13.6 

14.2 

14.8 

5 

154 

.16.1 

16.7 

17-3 

iS.o 

18.7 

19.4 

20.1 

20.8 

21-5 

6 

22.2 

23.0 

23-7 

245 

25.3 

26.1 

26.9 

27.7 

28.5 

29.4 

7 

3O.2 

3i.i 

32.0 

32-9 

33-8 

34-7 

35-7 

36.6 

37-6 

38.5 

8 

39-5 

40.5 

41-5 

42-5 

43-6 

44-6 

45-7 

46.7 

47-8 

48.9 

9 

50.0 

5i.  i 

52.2 

534 

54-5 

55-7 

56.9 

58.1 

59-3 

60.5 

10 

61.7 

63.0 

64.2 

65o 

66.8 

68.1 

69.4 

70.7          72.0 

73-3 

ii 

74-7 

76.1 

774 

78.8 

80.2 

81.6 

83-1 

84-5 

86.0 

874 

12 

88.9 

90.4 

91.9 

934 

94-9 

96.5 

98.0 

99-6 

IOI.I 

102.7 

*3 

104.3 

105.9 

107.6 

109.2 

1  10.8 

112.5 

114.2 

H5.9 

117.6 

II9-3 

I2I.O 

122.7 

124-5 

126.2 

128.0 

129.8 

131.6 

1334 

135.2 

137-0 

15 

138.9 

140.7 

142.6 

144-5 

146.4 

148.3 

150.2 

152.2 

I54-I 

156.1 

16 

158.0 

160.0 

162.0 

164.0 

166.0 

168.1 

170.1 

172.2 

174.2 

176.3 

17 

178.4 

180.5 

182.6 

184.7 

186.9 

189.0 

191.2 

1934 

195.6 

197.8 

18 

2OO.O 

2O2.2 

204.5 

206.7 

209.0 

211.3 

213.6 

215-9 

218.2 

220.5 

19 

222.8 

225.2 

227.6 

229.9 

232.3 

234.7 

237.1 

239.6 

242.0 

2445 

20 

246.9 

249.4 

251.9 

2544 

256.9 

2594 

262.0 

264-5 

267.1 

269.6 

21 

272.2 

274.8 

2774 

280.1 

282.7 

285.3 

288.0 

290.7 

2934 

296.1 

22 

298.8 

301-5 

304-2 

307-0 

309-7 

312.5 

315.3 

318.1 

320.9 

323-7 

23 

326.5 

3294 

332.2 

335-1 

338.0 

340-9 

343-8 

346.7 

349-7 

352.6 

24 

355-6 

358.5 

361.5 

364-5 

370.5 

373-6 

376.6 

379-7 

382.7 

25 

385/8 

388.9 

392.0 

395-1 

398.2 

401.4 

404-5 

407.7 

410.9 

414.1 

26 

417-3 

420.5 

4237 

427.0 

430.2 

433-5 

436.8 

440.1 

4434 

446.7 

27 

450.0 

453-3 

456.7 

460.1 

4634 

466.8 

470.2 

473-6 

477-1 

480.5 

28       484.0 

487.4 

490.9 

494-4 

497-9 

5014 

504-9 

508.5 

512.0 

515-6 

29 

5I9-I 

522.7 

526.3 

529-9 

533-6 

537-2 

540.8 

544-5 

548.2 

551-9 

30 

555-6 

559-3 

563-0 

566.7 

570.5 

574.2 

578.0 

581.8 

585-6 

5894 

31 

593-2 

597-0 

600.9 

604.7 

608.6 

612.5 

616.4 

620.3 

624.2 

628.2 

32 

632.1 

636.1 

640.0 

644.0 

648.0 

652.0 

656.0 

660.1 

664.1 

668.2 

33 

672.2 

676.3 

680.4 

684.5 

688.6 

692.7 

696.9 

701.0 

705.2 

709.4 

34 

713.6 

717-8 

722.0 

726.2 

730.5 

734-7 

739-0 

743-3 

747.6 

7519 

35 

756.2 

760.5 

764.8 

769.2 

773-6 

777-9 

782.3 

786.7 

791.1 

795-6 

36 

800.0 

804.5 

808.9 

813-4 

817.9 

822.4 

826.9 

831.4 

836.0 

840.5 

37 

845.1 

849.6. 

854.2 

858.8 

8634 

868.1 

872.7 

877-3 

882.0 

886.7 

38 

891.4 

896.1 

900.8 

905.5 

910.2 

915.0 

919.7 

924-5 

929-3 

934-1 

39 

938.9 

943-7 

943.5 

9534 

958.2 

963.1 

968.0 

972.9 

977-8 

982.7 

40 

987.7 

992.6 

997-6 

1002.5 

1007.5 

1012.5 

1017.5 

1022.5 

1027.6 

1032.6 

41 

1037-7 

1042.7 

1047.8 

1052.9 

1058.0 

1063.1 

1068.2 

10734 

1078.5 

1083.7 

42 

1088.9 

1094.1 

1099.3 

1104.5 

1109.7 

1115.0 

II2O.2 

1125.5 

1130.8 

1136.1 

43 

1141.4 

1146.7 

1152.0    1157.3 

1162.7 

1168.1 

II734 

1178.8    1184.2 

1189.6 

44 

1195.1 

1200.5 

1206.0 

1211.4 

1216.9 

12224 

1227.9 

1233.4    1238.9 

1244-5 

45 

1250.0 

1255-6 

1261.1 

1266.7 

1272.3 

1277.9 

1283.6 

1289.2    1294.8 

1300.5 

46 

1306.2 

1311.9 

1317-6 

1323-3 

1329-0 

1334-7 

1340.5 

1346.2    1352.0 

1357-8 

47 

1363.6 

1369.4 

1375-2 

1381.0 

1386.9 

1392.7 

1398.6 

1404.5    1410.4 

1416.3 

48 

1422.2 

1428.2 

I434-I 

1440.1 

1446.0 

1452-0 

1458.0 

1464.0  |  1470.0 

1476.1 

49 

1482.1 

1488.2 

1494.2 

1500.3 

1506.4 

1512.5 

I5I8.6 

1524-7 

1530.9 

1537-0 

50 

1543-2 

15494 

1555-6 

1561.8 

1568.0 

1574-2 

1580.5 

1586.7 

1593-0 

1599.3 

0. 

i. 

2. 

3- 

4- 

5- 

6. 

7- 

8. 

9- 

57 

TABLE  No.  5— CONCLUDED. 

Minus  Corrections  corresponding  to  JV~  JVr',  or  n~n',  and  general  for 
all  side  slopes.      For  confutation  by  average  Areas. 

Difference  of  Correction  numbers  in  feet  and  tenths  in  left  column  and 
at  top  /   Correction  in  cubic  yards  for  100  ft.  in  body  of  Table. 


<  *J 

\ 

II 

.0 

•3 

•4 

.5     -6 

•7     -8 

Q 

51 

1605.6 

1611.9 

1618.2 

1624.5 

1630.8 

1637.2 

1643.6 

1649.9  !656.3  i  1662.7 

52 

1669.1 

1675.6 

1682.0  1688.5 

1694.9  1701.4 

1707.9 

1714.4  1720.9 

1727.4 

53 

1734-0 

1740.5  1747.1  1753.6 

1760.2 

1766.8 

1773-4 

1780.1 

1786.7 

1793.3 

54 

1  800.0 

1806.7  1813.4 

1820.1 

1826.8 

T833-5 

1840.2 

1847.0 

1853-7 

1860.5  i 

55 

1867.3 

1874.1  1880.9  1887.7 

1894.5 

1901.4 

1908.2 

1915.1 

1922.0 

1928.9 

56 

1935.8 

1942.7  !  1949.7 

1956.6 

1963.6  1970.5 

I977.5 

1984.5 

I99L5 

1998.5 

57 

2005.6 

2OI2.6 

2019.7 

2026.7 

2033.8 

2040.9 

2048.0 

2055-1 

2062.2 

2069.4 

58 

2076.5 

2083.7 

2090.9 

2098.1 

2105.3 

2112.5 

2119.7 

2127.0 

2134-2 

2141.5 

59 

2148.8 

2I56.I 

2163.4 

2170.7 

2178.0 

2185.3 

2192.7 

2  2OO.  I 

2207.4 

2214.8 

60 

2222.2 

2229.6 

2237.1 

2244-5 

2252.0 

2259.4 

2266.9 

22744 

2281.9 

2289.4 

61 

2296.9 

2304.5 

2312.0 

2319.6 

2327.1 

2334-7  2342.3 

2349-9 

2357-6 

2365.2 

62 

2372.8 

2380.5 

2388.2 

2395-9 

2403.6 

2411.3  2419.0 

2426.7 

2434-5 

2442.2 

63 

2450.0 

2457-8 

2465.6 

2473-4 

2481.2 

2489.0 

2496.9 

2504.7 

2512.6 

2520.5 

64 

2528.4 

2536.3 

2544-2 

2552.2  2560.1 

2568.1 

2576.0 

2584-0 

2592.0 

2600.0 

65 

2608.0 

26lO.I 

2624.1 

2632.2  2640.2 

2648.3 

2656.4 

2664.5 

2672.6  2680.7 

66 

2688.9 

2697.0 

2705.2 

27134 

2721.6 

2729.8 

2738-0 

2746.2 

2754.5 

2762.7 

67 

2771.0 

2779-3 

2787.6 

2795-9 

2804.2 

2812.5 

2820.8 

2829.2 

2837.6 

2845-9 

68 

2854-3 

2862.7 

2871.1 

2879.6 

2888.0 

2896.5 

2904.9 

2913.4 

2921.9 

2930.4 

69 

2938.9 

29474 

2956.0 

2964-5 

2973.1 

2981.6 

2990.2 

2998.8  30074 

3016.1 

70 

3024.7 

3033-3 

3042.0 

3050.7 

3059-4 

3068.1 

3076.3  j  3085.5  j  3094.2 

3103.0 

71 

3III.7 

3120.5 

3129-3 

3I38.I 

3146.9 

3155.7 

3164.5  3173.4 

3182.2 

3191.1 

72 

32OO.O 

3203.9 

3217.8 

3226.7 

3235.7  3244.6 

3253.6  3262.5 

3271.5 

3280.5 

73 

3289.5 

3298.5 

3307.6 

3316.6 

3325.7 

3334-7 

3343-8  1  3352.9 

3362.0 

337I-I 

74 

3380.2 

33S94 

3398.5 

3407.7 

3416.9 

3426.1 

3435-3  i  3444-5 

3453-7 

3463-0 

75 

3472.2 

3481.5 

3490.8 

35oo.i 

3509.4 

3518.7 

3528.0 

3537-3 

3546.7 

3556.1 

76 

3565-4 

3574-8 

3584-2 

3593-6 

3603.1 

3612.5 

3622.0 

3631-4 

3640.9 

3650.4 

77 

3669.4 

3678.9 

3688.5 

3698.0 

3707.6 

37I7-I 

3726.7 

3736.3 

3745-9 

78 

3755-6 

3765.2 

3774-8 

3784.5 

3794-2 

3803.9 

3813-6 

3823-3 

3833-0 

3842-7 

79 

3852.5 

3862.2 

3872.0 

3881.8 

3891.6 

3901.4 

3911-2 

3921-0 

3930.9 

3940.7 

80 

3950.6 

3960.5 

3970.4 

3980.3 

3990.2 

4000.2  4010.1 

4020.1 

4030.0 

4040.0 

81 

4050.0 

4060.0  ]  4070.0 

4080.1 

4090.1 

4100.2 

4110.2 

4120.3 

4130.4 

4140.5 

82 

4150.6 

4160.7 

4170.9 

4181.0 

4191.2 

4201.4 

4211.6  i  4221.8 

4232.0 

4242.2 

83 

4252.5 

4262.7 

4273-0 

4283.3 

4293.6 

4303.9 

4314-2  4324.5 

4334-8 

4345-2 

84 

4355-6 

4365-9  |  4376.3 

4386.7 

4397-1 

4407.6 

4418.0  4428.5 

4438.9 

4449.4 

85 

4459-9 

4470.4  4480.9 

4491-4 

4502.0 

4512.5 

4523.1 

4533-6 

4544.2 

4554-8 

86 

45654 

4576.1 

4586.7 

4597-3 

4608.0 

4618.7 

4629.4  4640.1 

4650.8 

4661.5 

87 

4672.2 

4683.0 

4693-7 

4704.5 

47I5.3 

4726.1 

4736.9  4747-7 

4758.5 

47694 

88 

4780.2 

4791-1 

4802.0 

4812.9 

4823.8 

4834.7 

4845.7 

4856.6 

4867.6 

4878.5 

89 

4889.5 

4900.5 

49H-5 

4922.5 

4933-6 

4944.6 

4955-7 

4966.7 

4977-8 

4988.9 

go 

5000.0 

5011.1 

5022.2 

50334 

5044-5 

5055.7 

5066.9 

5078.1 

5089.3 

5100.5 

91 

5IH-7 

5123.0  5134.2 

5145.5 

5156.8 

5168.1 

5179-4 

5190.7 

5202.0 

5213.3 

!  92 

5224.7 

5236.1  5247.4 

5258.8 

5270.2 

5281.6 

5293.1 

5304.5 

53i6.o 

53274 

93 

5338.9 

5350.4  1  5361.9 

5373-4 

5384.9 

5396.5 

5408.0 

5419.6 

543LI 

5442.7 

94 

5454-3 

5465-9 

5477-6 

5489-2 

5500.8 

5512.5 

5524-2 

5535-9 

5547-6 

5559-3 

95 

5571-0 

5582.7 

5594-5 

5606.2 

5618.0 

5629.8 

5641-6 

56534 

5665.2 

5677.0 

96 

5688.9  5700.7 

5712.6 

5/24.5 

5736.4 

5748.3 

5760.2 

5772.2 

5784.1 

5796.1 

1  97 

5808.0 

5820.0 

5832.0 

5844.0 

5856.0 

5868.1 

5880.1 

5892.2 

5904.2 

59l6.3 

i  98 

5928.4 

5940.5 

5952.6 

5964.7 

5976.9 

5989-0 

6001.2 

6013.4 

6025.6 

6037.8 

,  99 

6050.0 

6062.2 

6074-5 

6086.7 

6099.0 

6111.3 

6123.6 

6135-9 

6148.2 

6160.5 

100 

6172.8 

6185.2 

6197.6 

6209.9 

6222.3 

6234.7 

6247.1 

6259.6 

6272.0 

6284.5 

.0 

,z 

.2 

•3 

.4 

•5 

.6 

.7 

.8 

•9 

58 


TABLE   No.  6.— LEVEL  CUTTINGS.     s-^-=~;  b=lQ  feet. 


A. 

.0 

.1 

.2     .3     -4     -5     -6 

•7     .8     .9   j 

o 

o.o 

5-9 

11.9 

17.8    23.8 

29.8 

35-8 

41.8 

47-9 

53-9 

I 

60.0 

66.1 

72.2 

78.3 

84.4 

90.6 

96.7 

102.9 

109.1 

II5-3 

2 

121.5 

127.7 

134-0 

140.2 

146.5 

152.8 

I59-1 

165.4 

171.7 

178.1 

3 

184.4 

190.8 

197.2 

203.6  !  2IO.O 

216.5 

222.9 

229.4 

235-9 

242.4 

4 

248.9 

255-4 

262.0 

268.5   275.1 

281.7 

288.3 

294.9 

301-5 

308.2 

5 

314.8 

321.5 

328.2 

334-9 

341.6 

348.3 

355.1 

361.8 

368.6 

375-4 

6 

382.2 

389-0 

395-9 

402.7 

409.6 

416.5 

4234 

430-3 

437-2 

444-2 

7 

451.1 

458.1 

465.1 

472.1 

479.1 

486.1 

493-2 

500.2 

507-3 

5M.4 

8 

521.5 

528.6 

535-7 

542.9 

550.0 

557-2 

5644 

571-6 

578.8 

586.1 

9 

593-3 

600.6 

607.9 

615.2 

622.5 

629.8 

637-2 

644-5 

651.9 

659-3 

10 

666.7 

674.1 

681.5 

689.0 

696.4 

703.9 

711.4 

718.9 

726.4 

733-9 

ii 

741.5 

749.0 

756.6 

764.2 

771.8 

779-4 

787.1 

794-7 

802.4 

Sio.i 

12 

817.8 

•825.5 

833.2 

841.0 

848.7 

856-5 

864.3 

872.1 

879.9 

887.7 

13 

895-6 

9034 

9H-3 

919.2 

927.1 

935-0 

942-9 

950-9 

958-8 

966.8 

14 

974.8 

982.8 

990.8 

998.9 

1007 

1015 

1023 

1031 

1039 

1047 

15 

1056 

1064 

1072 

I080 

1088 

1096 

1105 

ni3 

II2I 

1129 

16 

1138 

1146 

H54 

1163 

1171 

1179 

1188 

1196 

1205 

1213 

17 

1221 

1230 

1238 

1247 

1255 

1264 

1272 

1281 

1290 

1298 

18 

1307 

13*5 

1324 

1333 

1341 

1350 

1358 

1367 

1376 

1385 

19 

1393 

1402 

1411 

1420 

1428 

1437 

1446 

1455 

1464 

1473 

20 

I482 

1490 

1499 

1508 

1517 

1526 

1535 

1544 

1553 

1562 

21 

1571 

1580 

1589 

1598 

1607 

1616 

1626 

1635 

1644 

1653 

22 

l662 

1671 

1681 

1690 

1699 

1708 

1718 

1727 

1736 

1745 

23 

1755 

1764 

1774 

1783 

1792 

1802 

1811 

1821 

1830 

1839 

24 

1849 

1858 

1868 

1877 

1887 

1896 

1906 

1916 

1925 

1935 

25 

1944 

1954 

1964 

1973 

1983 

1993 

2OO2 

2012 

2022 

2032 

25 

2041 

2051 

2061 

2071 

2081 

2091 

2IOO 

2110 

2I2O 

2130 

27 

2I4O 

2150 

2160 

2I"O 

2180 

2190 

2200 

22IO 

222O 

2230 

23 

224O 

2250 

2260 

2270 

2280 

2291 

23OI 

23H 

2321 

233i 

29 

2341 

2352 

2362 

2372 

2382 

2393 

2403 

2413 

2424 

2434 

3° 

2444 

2455 

2465 

2476 

2486 

2496 

2507 

2517 

2528 

2538 

31 

2549 

2559 

2570 

2581 

2591 

2602 

2612 

2623 

2634 

2644 

S2 

2655 

2665 

2676 

2687 

2698 

2708 

2719 

2730 

2741 

2751 

33 

2762 

2773 

2784 

2795 

2806 

2816 

2827 

2838 

2849 

2860 

34 

2871 

2882 

2893 

2904 

2915 

2926 

2937 

2948 

2959 

2970 

35 

2981 

2993 

3004 

3015 

3026 

3037 

3048 

3060 

3071 

3082 

36 

3093 

3105 

3116 

3127 

3138 

3150 

3l6l 

3173 

3184 

3195 

37 

3207 

3218 

3230 

3241 

3252 

3264 

3275 

3287 

3298 

33io 

38 

3321 

3333 

3345 

3356 

3368 

3379 

3391 

3403 

3414 

3426 

39 

3433 

3449 

346i 

3473 

3485 

3496 

3508 

3520 

3532 

3544 

40 

3556 

3567 

3579 

358i 

3593 

3605 

3617 

3629 

3641 

3653 

4i 

3675 

3687 

3699 

37ii 

3723 

3735 

3747 

3759 

3771 

3783 

42 

3796 

3808 

3820 

3832 

3844 

3856 

3869 

3881 

3893 

3905 

43 

39i3 

3930 

3942 

3955 

3967 

3979 

3992 

4004 

4017 

4029 

44 

4041 

4054 

4066 

4079 

4091 

4104 

4116 

4129 

4142 

4154 

45 

4167 

4179 

4192 

4205 

4217 

4230 

4242 

4255 

4268 

4281 

46 

4293 

4306 

4319 

4332 

4344  • 

4357 

4370 

4383 

4396 

4409 

47 

4421 

4434 

4447 

4460 

4473 

4486 

4499 

4512 

4525 

4538 

48 

4551 

4564 

4577 

4590 

4603 

4616 

4630 

4643 

4656 

4669 

49 

4682 

4695 

4709 

4722 

4735 

4748 

4762 

4775 

4788 

4801 

5° 

4815 

4828 

4842 

4855 

4868 

4882 

4895 

4909 

4922 

4935 

5i 

4949 

4962 

4976 

4989 

5003 

5016 

5030 

5044 

5057 

5071 

52 

5084 

5098 

5H2 

5125 

5139 

5153 

5166 

5180 

5194 

5208 

53 

5221 

5235 

5249 

5263 

5277 

5291 

5304 

53i8 

5332 

5346 

54 

536o 

5374 

5388 

5402 

54i6 

5430 

5444 

5458 

5472 

5486 

55 

5500 

5514 

5528 

5542 

5556 

5571 

5585 

5599 

5613 

5627 

56 

5641 

5656 

5670 

5684 

5698 

5713 

5727 

574i 

5756 

5770 

57 

5784 

5799 

58i3 

5828 

5842 

5856 

5871 

5885 

5900 

5914 

58 

5929 

5943 

5958 

5973 

5987 

6002 

6016 

6031 

6046 

6060 

59 

6075 

6089 

6104 

6119 

6i34 

6148 

6163 

6178 

6193 

6207 

60 

6222 

6237 

6252 

6267 

6282 

6296 

6311 

6326 

6341 

6356 

.0 

.1 

.2 

•3 

•4 

•5 

.6 

.7 

.8 

•9 

59 


TABLE  No.  7.—  LEVEL   CUTTINGS.     --=~-  b=2S  feet. 


£ 

.0 

.1 

.2 

•3   f 

.4 

•5 

.6 

•7 

.8 

-9 

0 

0.0 

10.4 

20.8 

31-2 

41.6 

52.0 

62.5 

73-0 

83-4 

93-9 

I 

104.4 

115.0 

125.5 

136.1 

146.6 

157-2 

167.8 

178.4 

189.1 

199.7 

2 

210.4 

221.0 

231.7 

242.4 

253-2 

263.9 

274.6 

2854 

296.2 

307-0 

3 

317.8 

328.6 

339-4 

350.3 

361.2 

372.0 

382.9 

393-8 

404.8 

4T5.7 

4 

426.7 

437-6 

448.6 

459-6 

470.6 

481.7 

492-7 

503-8 

514.8 

525-9 

5 

537-0 

548.2 

559-3 

570.4 

581.6 

592-8 

604.0 

615.2 

626.4 

637-6 

6 

648.9 

660.2 

671.4 

682.7 

694.0 

7054 

716.7 

728.1 

739-4 

750.8 

7 

762.2 

773-6 

785-1 

796.5 

808.0 

819.4 

830.9 

842.4 

854.0 

865.5 

8 

877.0 

888.6 

900.2 

911.8 

9234 

935-0 

946.6 

958.3 

970.0 

981.6 

9 

993-3 

1005 

1017 

1029 

1040 

1052 

1064 

1076 

1087 

1099 

10 

mi 

1123 

1135 

1147 

H59 

1171 

1182 

1194 

1206 

1218 

ii 

1230 

1242 

1254 

1266 

1278 

1291 

1303 

1315 

1327 

1339 

12 

1351 

1363 

1375 

1388 

1400 

1412 

1424 

1437 

1449 

1461 

I3 

1473 

1486 

1498 

1510 

1523 

1535 

1547 

1560 

1572 

1585 

14 

1597 

1609 

1622 

1634 

1647 

1659 

1672 

1685 

1697 

1710 

15 

1722 

1735 

1747 

1760 

1773 

1785 

1798 

1811 

1823 

1836 

16 

1849 

1862 

1874 

1887 

1900 

I9X3 

1926 

1938 

1951 

1964 

17 

1977 

1990 

2003 

2016 

2029 

2042 

2055 

2068 

2081 

2094 

18 

2107 

2120 

2133 

2146 

2159 

2172 

2185 

2198 

2211 

2225 

19 

2238 

2251 

2264 

2277 

2291 

2304 

2317 

2330 

2344 

2357 

20 

2370 

2384 

2397 

2410 

2424 

2437 

2451 

2464 

2478 

2491 

21 

2504 

2518 

2531 

2545 

2558 

2572 

2586 

2599 

2613 

2626 

22 

2640 

2654 

2667 

2681 

2695 

2708 

2722 

2736 

2750 

2763 

23 

2777 

2791 

2805 

2818 

2832 

2846 

2860 

2874 

2888 

2902 

24 

2916 

2929 

2943 

2957 

2971 

2985 

2999 

3013 

3027 

3041 

25 

3056 

3070 

3084 

3098 

3112 

3126 

3140 

3154 

3169 

3183 

26 

3197 

3211 

3226 

3240 

3254 

3268 

3283 

3297 

33ii 

3326 

27 

3340 

3354 

3369 

3383 

3398 

3412 

3426 

3441 

3455 

3470 

28 

3434 

3499 

35H 

3528 

3543 

3557 

3572 

3586 

3601 

3616 

29 

3630 

3645 

3660 

3674 

3689 

3704 

3719 

3733 

3748 

3763 

30 

3778 

3793 

3807 

3822 

3837 

3852 

3867 

3882 

3897 

3912 

31 

3927 

3942 

3957 

3972 

3987 

4002 

4017 

4032 

4047 

4062 

32 

4077 

4092 

4107 

4122 

4138 

4153 

4168 

4183 

4198 

4214 

33 

4229 

4244 

4259 

4275 

4290 

4305 

4321 

4336 

4351 

4367 

34 

4382 

4398 

4413 

4429 

4444 

4459 

4475 

4490 

4506 

4521 

35 

4537 

4553 

4568 

4584 

4599 

46i5 

4631 

4646 

4662 

4678 

36 

4693 

4709 

4725 

474i 

4756 

4772 

4788 

4804 

4819 

4835 

37 

4851 

4867 

4883 

4899 

4915 

4931 

4946 

4962 

4978 

4994 

38 

5010 

5026 

5042 

5058 

50/4 

5091 

5107 

5123 

5139 

5155 

39 

5i7i 

5i87 

5203 

5220 

5236 

5252 

5268 

5285 

5301 

5317 

40 

5333 

5350 

5366 

5382 

5399 

5415 

5431 

5448 

5464 

548i 

41 

5497 

5513 

5530 

5546 

5563 

5579 

5596 

5613 

5629 

5646 

42 

5662 

5679 

5695 

5712 

5729 

5745 

5762 

5779 

5795 

5812 

43 

5829 

5846 

5862 

5879 

5896 

59*3 

5930 

5946 

5963 

5980 

44 

5997 

6014 

6031 

6048 

6065 

6082 

6099 

6116 

6i33 

6150 

45 

6167 

6184 

6201 

6218 

6235 

6252 

6269 

6286 

6303 

6321 

46 

6338 

6355 

6372 

6389 

6407 

6424 

6441 

6458 

6476 

6493 

47 

6510 

6528 

6545 

6562 

6580 

6597 

6615 

6632 

6650 

6667 

48 

6684 

6702 

6719 

6737 

6754 

6772 

6790 

6807 

6825 

6842 

49 

6860 

6878 

6895 

6913 

6931 

6948 

6966 

6984 

7002 

7019 

50 

7037 

7055 

7073 

7090 

7108 

7126 

7144 

7162 

7180 

7198 

5i 

7216 

7233 

7251 

7269 

7287 

7305 

7323 

7341 

7359 

7377 

52 

7396 

7414 

7432 

7450 

7468 

7486 

7504 

7522 

7541 

7559 

53 

7577 

7595 

7614 

7632 

7650 

7668 

7687 

7705 

7723 

7742 

54 

7760 

7778 

7797 

7815 

7834 

7852 

7870 

7889 

79°7 

7926 

55 

7944 

7963 

7982 

8000 

8019 

8037 

8056 

8074 

8093 

8112 

56 

8130 

8i49 

8168 

8186 

8205 

8224 

8243 

8261 

8280 

8299 

57 

8318 

8337 

8355 

8374 

8393 

8412 

8431 

8450 

8469 

8488 

58 

8507 

8526 

S545 

8564 

8583 

8602 

8621 

8640 

8659 

8678 

59 

8697 

8716 

8735 

8754 

8774 

8793 

8812 

8831 

8850 

8870 

60 

8889 

8908 

8927 

8947 

8966 

8985 

9°°5 

9024 

9°43 

9063 

.0 

.1 

.2 

•3 

.4 

i   -5 

.6 

•7 

.8 

•9 

60 

TABLE  No.  8. 
Plus  Corrections  for  -i—— 5* 


1 

0. 

i. 

2. 

3- 

4- 

5- 

6. 

7- 

8. 

9- 

o 

0.0 

0.0 

0.0 

0.0 

0.0 

o.o 

• 
o.o 

o.o 

o.o 

O.I 

I 

O.I 

O.I 

O.I 

O.I 

O.I 

O.I 

0.2 

0.2 

0.2 

0.2 

2 

0.3 

0.3 

03 

0.3 

0.4 

0.4 

0.4 

0-5 

0-5 

0-5 

3 

0.6 

0.6 

0.6 

0.7 

0.7 

0.8 

0.8 

0.9 

0.9 

O.Q 

4 

I.O 

I.O 

i.i 

i.i 

1.2 

i-3 

1-3 

1.4 

1.4 

i-5 

5 

1-5 

1.6 

1-7 

1-7 

1.8 

1.9 

1.9 

2.0 

2.1 

2.2 

6 

2.2 

-2.3 

2.4 

2-5 

2-5 

2.6 

2-7 

2.8 

2.9 

2.9 

7 

3-0 

3-i 

3-2 

3-3 

3-4 

3-5 

3-6 

3.7 

3-8 

3.9 

8 

4.0 

4.1 

4.2 

4.3 

44 

4-5 

4.6 

4.7 

4.8 

4.9 

9 

5-o 

5-1 

5-2 

5-3 

5-5 

5-6 

5-7 

5-8 

5-9 

6.1 

10 

6.2 

6-3 

6.4 

6.6 

6.7 

6.8 

6.9 

7-i 

7-2 

7-3 

ii 

7-5 

7-6 

7-7 

7-9 

8.0 

8.2 

8-3 

8-5 

8.6 

8-7 

12 

8.9 

9.0 

9.2 

9-3 

9-5 

9-7 

9.8 

10.0 

10.  1 

10.3 

13 

10.4 

10.6 

10.8 

10.9 

ii.  I 

H-3 

11.4 

n.6 

n.8 

11.9 

14 

12.  1 

12.3 

12.5 

12.6 

12.8 

13-0 

13-2 

13-3 

13-5 

13.7 

15 

13-9 

14.1 

14-3 

14-5 

14.6 

14.8 

15-0 

15-2 

154 

15.6 

16 

15-8 

16.0 

16.2 

16.4 

16.6 

16.8 

17.0 

17.2 

17.4 

17.6 

17 

I7.8 

iS.i 

18.3 

18.5 

18.7 

18.9 

19.1 

19-3 

19.6 

19.8 

18 

2O.O 

20.2 

20.5 

20.7 

20.9 

21.  1 

21.4 

21.6 

21.8 

22.1 

ig 

22.3 

22.5 

22.8 

23.0 

23.2 

23-5 

23-7 

24.0 

24.2 

24-5 

20 

•   24.7 

24-9 

25-2 

25-4 

25.7 

25-9 

26.2 

26.5 

26.7 

27.0 

21 

27.2 

27-5 

27-7 

28.0 

28.3 

28.5 

28.8 

29.1 

29-3 

29.6 

22 

29.9 

30.2 

30-4 

30.7 

31-0 

31.3 

31-5 

31-8 

32.1 

324 

23 

32.7 

32.9 

33-2 

33-5 

33-8 

34-1 

34-4 

34-7 

35-0 

35-3 

24 

35-6 

35-9 

36.2 

36.5 

36.8 

37-1 

37-4 

37-7 

38.0 

38.3 

25 

38.6 

38.9 

39-2 

39-5 

39-8 

40.1 

40.5 

40.8 

41.1 

41.4 

26 

41.7 

42.1 

42.4 

42.7 

43-0 

434 

43-7 

44.0 

44-3 

44-7 

27 

45-o 

45-3 

45-7 

46.0 

46.3 

46.7 

47.0 

474 

47-7 

48.1 

28 

48.4 

48.7 

49-1 

49-4 

49-8 

50.1 

50.5 

50-9 

51.2 

51.6 

29 

51-9 

52.3 

52.6 

53-o 

53-4 

53-7 

54-1 

54-5 

54-8 

55-2 

30 

55-6 

55-9 

56.3 

56.7 

57-1 

57-4 

57-8 

58.2 

58.6 

58.9 

31 

59-3 

59-7 

60.  i 

60.5 

60.9 

61.3 

61.6 

62.0 

62.4 

62.8 

32 

63.2 

63.6 

64.0 

644 

64.8 

65.2 

65.6 

66.0 

66.4 

66.8 

33 

67.2 

67.6 

68.0 

68.5 

68.9 

69-3 

69-7 

70.1 

70.5 

70.9 

34 

71.4 

71.8 

72.2 

72.6 

73-1 

73-5 

73-9 

74-3 

74-8 

75-2 

35 

75.6 

76.1 

76.5 

76.9 

774 

77-8 

78.2 

78.7 

79.1 

79-6 

36 

80.0 

80.5 

80.9 

81.3 

81.8 

82.2 

82.7 

83.1 

83-6 

84.1 

37 

84.5 

85.0 

854 

85-9 

86.3 

86.8 

87.3 

87.7 

88.2 

88.7 

38 

89.1 

89.6 

90.1 

90.6 

91.0 

9L5 

92.0 

92.5 

92.9 

934 

39 

93-9 

944 

94-9 

95-3 

95-8 

96.3 

96.8 

97-3 

97.8 

98.3 

40 

98.8 

99-3 

99-8 

100.3 

100.8 

101.3 

101.8 

102.3 

102.8 

103.3 

0. 

i. 

2. 

3- 

4- 

5- 

6. 

7- 

8. 

9. 

NOTE.— The  quantities  in  the  above  table  multiplied  by  2  give  the  minus 

*-4-s'     1 
corrections  for-—  =  •• 


61 


TABLE  Xo.  9.—  LEVEL  CUTTINGS.  =;  &  =  1G 


fc 

o. 

I. 

2. 

3. 

4-     5- 

6-     7- 

8. 

9- 

0 

o.o 

5.9 

n.g 

17.9 

24.0   30.1 

36.2 

42.4 

48.6   54-8 

I 

6z.i 

67.4 

73-8 

80.2 

S6.6j   93.1 

99-6 

1  06.  i 

112.7 

119.3 

2 

125.9 

132.6 

139-3 

146.1 

152  g 

159-7 

166.6 

173-5 

180.4 

187.4 

3 

194.4 

201.5 

208.6 

215.7 

222.C 

230.1 

237-3 

244.6 

251-9 

259-3 

4 

266.7 

274.1 

281.6 

289.1 

296.6 

304.2 

3H.8 

3I9-4 

327.1 

334-8 

5 

342.6 

350.4 

358.2 

366.1 

374-0 

381.9 

389-9 

397-9 

406.0 

414.1 

6 

422.2 

430.4 

438.6 

446.8 

455.1 

463-^ 

471.8 

480.2 

488.6 

497-1 

7 

505-6 

5I4.I 

522.7 

531-3 

539-9 

548.6 

557-3 

566.1 

574-9 

583.7 

8 

592-6 

601.5 

610.^ 

619.41  628.^ 

637.5 

646.6 

655-7 

664.9 

674.1 

9 

683.3 

692.6 

701.  c 

7II-3 

720.7 

730.1 

739-6 

749.1 

758.6 

768.2 

10 

777-8 

7874 

797.1 

806.8 

816.6 

826.4 

836.2 

846.1 

856.0 

865.9 

ii 

875-9 

885.9 

896.0 

906.1 

916.2 

926.^ 

936.6 

946.8 

957-1 

967.4 

12 

977.8 

988.2 

998.6 

1009 

IO2O 

1030 

1041 

1051 

1062 

1073 

13 

1083 

1094 

1105 

1116 

1127 

1138 

1148 

H59 

1170 

1182 

H 

H93 

1204 

1215 

1226 

1237 

1249 

1260 

1271 

1283 

1294 

15 

1306 

1317 

1329 

1340 

1352 

1363 

1375 

1387 

1399 

1410 

16 

1422 

1434 

1446 

1458 

1470 

1482 

1494 

1506 

1518 

1530 

17 

1543 

1555 

1567 

1579 

1592 

1604 

1617 

1629 

1642 

1654 

i3 

1667 

1679 

1692 

1705 

1717 

1730 

1743 

1756 

1769 

1782 

19 

1794 

1807 

1820 

1834 

1847 

1860 

1873 

1886 

1899 

1913 

20 

1926 

1939 

1953 

1966 

1980 

1993 

2007 

2020 

2034 

2047 

21 

2061 

2075 

2089 

2IO2 

2116 

2130 

2144 

2158 

2172 

2186 

22 

2200 

2214 

2228 

2242 

2257 

2271 

2285 

2299 

2314 

2328 

23 

2343 

2357 

2372 

2386 

2401 

2415 

2430 

2445 

2459 

2474 

24 

2489 

2504 

2519 

2534 

2548 

2563 

2578 

2594 

2609 

2624 

25 

2639 

2654 

2669 

2685 

2700 

2715 

2731 

2746 

2762 

2777 

26 

2793 

2808 

2824 

2839 

2855 

2871 

2887 

2902 

2918 

2934 

27 

2950 

2966 

2982 

2998 

3014 

3030 

3046 

3062 

3079 

3095 

28 

SHI 

3127 

3144 

3160 

3177 

3193 

3210 

3226 

3243 

3259 

29 

3276 

3293 

3309 

3326 

3343 

336o 

3377 

3394 

3410 

3427 

30 

3444 

3462 

3479 

3496 

3513 

3530 

3547 

3565 

3582 

3599 

31 

3617 

3634 

3652 

3669 

3687 

3704 

3722 

3739 

3757 

3775 

32 

3793 

3810 

3828 

3846 

3864 

3882 

39°o 

39i8 

3936 

3954 

33 

3972 

3990 

4009 

4027 

4045 

4063 

4082 

4100 

4119 

4137 

34 

4156 

4174 

4193 

4211 

4230 

4249 

4267 

4286 

4305 

4324 

35 

4343 

4362 

4380 

4399 

4418 

4438 

4457 

4476 

4495 

4514 

36 

4533 

4553 

4572 

4591 

4611  - 

4630 

4650 

4669 

4689 

4708 

37 

4728 

4747 

4767 

4787 

4807 

4826 

4846 

4866 

4886 

4906 

38 

4926 

4946 

4966 

4986 

5006 

5026 

5047 

5067 

5087 

5107 

39 

5128 

5148 

5169 

5189 

5210 

5230 

5251 

5271 

5292 

5313 

40 

5333 

5354 

5375 

5396 

5417 

5438 

5458 

5479 

55oo 

5522 

4i 

5543 

5564 

5585 

5606 

5627 

5649 

5670 

5691 

5713 

5734 

42 

5756 

5777 

5799 

5820 

5842 

5863 

5885 

5907 

5929 

5950 

43 

5972 

5994 

6016 

6038 

6060 

6082 

6104 

6126 

6148 

6170 

44 

6193 

6215 

6237 

6259 

6282 

6304 

6327 

6349 

6372 

6394 

45 

6417 

6439 

6462 

6485 

6507 

6530 

6553 

6576 

6599 

6622 

46 

6644 

6667 

6690 

6714 

6737 

6760 

6783 

6806 

6829 

6853 

47 

6876 

6899 

6923 

6946 

6970 

6993 

7017 

7040 

7064 

7087 

48 

7111 

7135 

7159 

7182 

7206 

7230 

7254 

72/8 

7302 

7326 

49 

7350 

7374 

7398 

7422 

7447 

7471 

7495 

7519 

7544 

7568 

50 

7593 

7617 

7642 

7666 

7691 

7715 

7740 

7765 

7789 

7814 

51 

7839 

7864 

7889 

7914 

7938 

7963 

7988 

8014 

8039 

8064 

52 

8089 

8114 

8i39 

8165 

8190 

8215 

8241 

8266 

8292 

8317 

53 

8343 

8368 

8394 

8419 

8445 

8471 

8497 

8522 

8548 

8574 

54 

8600 

8626 

8652 

8678 

8704 

8730 

8756 

8782 

8809 

8835 

55 

8861 

8887 

8914 

8940 

8967 

8993 

9020 

9046 

9°73 

9099 

56 

9126 

9*53 

9179 

9206 

9233 

9260 

9287 

9314 

9340 

9367 

57 

9394 

9422 

9449 

9476 

9503 

9530 

9557 

9585 

9612 

9639 

58 

9667 

9694 

9722 

9749 

9777 

9804 

9832 

9859 

9887 

9915 

59 

9943 

9970 

9998 

10026 

10054 

10082 

OIIO 

0138 

10166 

0194 

60 

IO222 

10250 

10279 

10307 

10335 

10363 

0392 

0420 

10449 

0477 

.O 

.1 

.2 

•3 

•4 

•5 

.6 

-7   1   -8 

•9 

62 
TABLE  KG.   10.— LEVEL  CUTTIXG.S. 


£ 

.0 

.1      .2   |   .3 

-4     -5     .6     .7   |   .8   1   .9 

o 

0. 

10.4 

20.8 

31-3 

41.8 

52.3 

62.9 

73-5 

84,1 

94-8 

I 

105.6 

Il6.3 

127.1 

137-9 

148.8 

159-7 

170.7 

181.6 

192.7 

203.7 

2 

214.8 

225.9 

237.1 

248.3 

259.6 

270.8 

282.1 

293.5 

304-9 

316.3 

3 

327.8 

339-3 

350.8 

362.4 

374-0 

385-6 

397-3 

409.1 

420.8 

432-6 

4 

444-4 

456.3 

468.2 

480.2 

492.1 

504.2 

516.2 

528.3 

540.4 

552.6 

5 

564-8 

577-1 

589.3 

601.6 

614.0 

626.4 

638.8 

651-3 

663.8 

676.3 

6 

688.9 

701.5 

714.1 

7268 

739-6|  752.3 

765-1 

777-9 

790.8 

803.7 

7 

816.7 

829.6 

842.7 

855-7 

868.8 

881.9 

895.1 

908.3 

921.6 

934-8 

8 

948.1 

961.5 

974.9 

988.3 

IOO2 

1015 

1029 

1042 

1056 

1070 

9 

1083 

1097 

mi 

1125 

H38 

1152 

1166 

1180 

1194 

1208 

10 

1222 

1236 

1250 

1265 

1279 

1393 

1307 

1322 

1336 

1350 

ii 

1365 

1379 

1394 

1408 

1423 

1438 

1452 

1467 

1482 

1496 

12 

IS" 

1526 

1541 

1556 

1571 

1586 

1601 

1616 

1631 

1646 

13 

1661 

•  1676 

1692 

1707 

1/22 

1738 

1753 

1768 

1784 

1799 

Z4 

1815 

1830 

1846 

IS62 

I877 

1893 

1909 

1925 

1940 

1956 

15 

1972 

1988 

2004 

2020 

2036 

2052 

2068 

2085 

2IOI 

2117 

16 

2133 

2150 

2166 

2182 

2199 

2215 

2232 

2246 

2265 

2282 

I? 

2298 

2315 

2332 

2348 

2365 

2382 

2399 

2416 

2433 

2450 

18 

2467 

2484 

2501 

2518 

2535 

2552 

2570 

2587 

2604 

2622 

19 

2639 

2656 

2674 

2691 

2709 

2726 

2744 

2762 

2779 

2797 

20 

2815 

2833 

2850 

2868 

2886 

2904 

2922 

2940 

2958 

2976 

21 

2994 

3013 

3031 

3049 

3067 

3086 

3104 

3122 

3Mi 

3159 

22 

3178 

3196 

3215 

3234 

3252 

3271 

3290 

3308 

3327 

3346 

23 

3365 

3384 

3403 

3422 

3441 

3460 

3479 

3498 

3517 

3536 

24 

3556 

3575 

3594 

3614 

3633 

3652 

3672 

3691 

37U 

3730 

25 

3750 

3770 

3789 

3809 

3829 

3849 

3868 

3888 

3908 

3928 

26 

3946 

3968 

3988 

4008 

4028 

4049 

4069 

4089 

4109 

4130 

27 

4150 

4170 

4191 

4211 

4232 

4252 

4273 

4294 

4314 

4335 

28 

4356 

4376 

4397 

4418 

4439 

4460 

4481 

4502 

4523 

4544 

29 

4565 

4586 

4607 

4628 

4650 

4671 

4692 

4714 

4735 

4756 

30 

47/8 

4799 

4821 

4842 

4864 

4886 

4907 

4929 

4951 

4973 

31 

4994 

5016 

5038 

5O6O 

5082 

5104 

5126 

5U8 

5i7o 

5193 

32 

5215 

5237 

5259 

5282 

5304 

5326 

5349 

5371 

5394 

54i6 

33 

5439 

5462 

5484 

5507 

5530 

5552 

5575 

5598 

5621 

5644 

34 

5667 

5690 

5713 

5736 

5759 

5782 

5805 

5828 

5852 

5875 

35 

5898 

5922 

5945 

5968 

5992 

6015 

6039 

6062 

6086 

6no 

36 

6i33 

6i57 

6181 

6205 

6228 

6252 

6276 

6300 

6324 

6348 

37 

6372 

6396 

6420 

6445 

6469 

6493 

6517 

6542 

6566 

6590 

38 

6615 

6639 

6664 

6688 

6713 

6738 

6762 

6787 

6812 

6836 

39 

6861 

6886 

6911 

6936 

6961 

6986 

7011 

7036 

7061 

7086 

40 

7111 

7136 

7162 

7187 

7212 

7238 

7263 

7288 

73U 

7339 

4i 

7365 

7390 

7416 

7442 

7467 

7493 

7519 

7545 

7570 

7596 

42 

7622 

7648 

7674 

7700 

7726 

7752 

j.-.-Q 

777° 

7805 

7831 

7857 

43 

7883 

7910 

7936 

7962 

7989 

8015 

8042 

8068 

8095 

8122 

44 

8148 

8i75 

8202 

8228 

8255 

8282 

8309 

8336 

8363 

8390 

45 

8417 

8444 

8471 

8498 

8525 

8552 

8580 

8607 

8634 

8662 

46 

8689 

8716 

8744 

8771 

8799 

8826 

8854 

8882 

8909 

8937 

47 

8965 

8993 

9020 

9048 

9076 

9104 

9132 

9160 

9188 

9216 

48 

9244 

9273 

9301 

9329 

9357 

9386 

9414 

9442 

9471 

9499 

49 

9528 

9556 

9585 

9614 

9642 

9671 

9700 

9728 

9757 

9786 

50 

9815 

9844 

9873 

9902 

9931 

9960 

9989 

10018 

10047 

10076 

5i 

10106 

ioi35 

10164 

10194 

10223 

10252 

10282 

10311 

10341 

10370 

52 

10400 

10430 

10459 

10489 

10519 

10549 

10578 

10608 

10638 

10668 

53 

10698 

10728 

10758 

10788 

10818 

10849 

10879 

10909 

10939 

10970 

54 

IIOOO 

11030 

11061 

11091 

III22 

11152 

11183 

11214 

11244 

11275 

55  11306 

11336 

11367 

11398 

II429 

11460 

11491 

11522 

"553 

11584 

56 

11615 

11646 

11677 

11708 

II740 

11771 

11802 

n834 

11865 

11896 

57 

11928 

"959 

11991 

I2O22 

12054 

12086 

12117 

12149 

12181 

12213 

58 

12244 

12276 

12308 

12340 

12372 

12404 

12436 

12468 

12500 

12533 

59 

12565 

12597 

12629 

12662 

12694 

12726 

i*759 

12791 

12824 

12856 

60 

12889 

12922 

12954 

12987 

13020 

13052 

13^5 

13118 

13151 

13184 

.0 

.1 

.2 

•3 

•4 

•5 

.6 

-7 

.8 

-9 

63 


TABLE  Xo.  11. 


Plus  Corrections  for  -—•  = 


1 

.0 

.1 

.2 

.3 

.4 

-5 

.6 

d  - 

•9 

o 

o. 

O. 

0. 

0. 

0. 

0. 

O.I 

O.I 

O.I 

O.I 

I 

O.2 

O.2 

O.2 

0.3 

0-3 

0.3 

0.4 

0.4 

0.5 

0.6 

2 

0.6 

0.7 

0.7 

0.8 

0.9 

I.O 

I.O 

i.i 

1.2 

1.3 

3 

1.4 

1.5 

1.6 

1.7 

1.8 

1.9 

2.0 

2.1 

2.2 

2-3 

4 

2.5 

2.6 

2.7 

2-9 

3-0 

3-1 

3-3 

34 

3-6 

3-7 

5 

3.9 

4.0 

4-2 

4-3 

4-5 

4-7 

4.8 

5-0 

5-2 

54 

6 

5-6 

5-7 

5-9 

6.1 

6-3 

6-5 

6.7 

6-9 

7-i 

7-3 

7 

7-6 

7-8 

8.0 

8.2 

8-5 

8-7 

8.9 

9.1 

94 

9.6 

8 

9.9 

IO.I 

10.4 

10.6 

10.9 

ii.  i 

11.4 

11.7 

12.0 

12.2 

9 

12.5 

12.8 

I3-I 

13-3 

13.6 

13-9 

14.2 

14-5 

14-8 

I5-I 

10 

15-4 

15.7 

16.1 

16.4 

16.7 

17.0 

17-3 

17.7 

iS.o 

18.3 

ii 

18.7 

19.0 

19.4 

19.7 

20.  i 

20.4 

20.8 

21.  1 

21-5 

21.9 

12 

22.2 

22.6 

23.0 

23-3 

23-7 

24.1 

24.5 

24-9 

25.3 

25-7 

13 

26.1 

26.5 

26.9 

27.3 

27.7 

28.1 

28.5 

29.0 

29.4 

29.8 

14 

30.2 

30-7 

31.1 

31-6 

32.0 

32.4 

32.9 

33-3 

33.8 

34-3 

15 

34-7 

35-2 

35-7 

36.1 

36.6 

37-1 

37-6 

38.0 

38.5 

39-0 

16 

39-5 

40.0 

40.5 

41.0 

41-5 

42.0 

42.5 

43-0 

43-6 

44-1 

17 

44-6 

45-1 

45-7 

46.2 

46.7 

47-3 

47-8 

48.3 

48.9 

494 

k  18 

50.0 

50.6 

51-1 

51.7 

52.2 

52.8 

534 

54-0 

54-5 

55-i 

19 

55-7 

56-3 

56.9 

57-5 

58.1 

58.7 

59-3 

59-9 

60.5 

61.1 

20 

61.7 

62.3 

63.0 

63.6 

64.2 

64.9 

65.5 

66.1 

66.8 

674 

21 

68.1 

68.7 

89.4 

70.0 

70.7 

71-3 

72.0 

72.7 

73-3 

74-0 

22 

74-7 

75-4 

76.1 

76-7 

774 

78.1 

78.8 

79-5 

80.2 

80.9 

23 

81.6 

82.3 

83.1 

83.8 

84.5 

85-2 

86.0 

86.7 

87.4 

88.1 

24 

88.9 

89.6 

90.4 

91.1 

91.9 

92.6 

934 

94.1 

94-9 

95-7 

25 

96.5 

97.2 

98.0 

98.8 

99-6 

100.3 

IOI.I 

101.9 

102.7 

103-5 

26 

104.3 

105.1 

105.9 

106.7 

107.6 

108.4 

109.2 

IIO.O 

no.S 

in.  7 

27 

112.5 

II3-3 

114.2 

115.0 

II5-9 

116.7 

117.6 

118.4 

II9-3 

1  20.  i 

28 

I2I.O 

.121.9 

122.7 

123.6 

124-5 

125-3 

126.2 

127.1 

128.0 

128.9 

29 

129.8 

130.7 

131.6 

132.5 

133-4 

134-3 

135-2 

136.1 

137-0 

138.0 

30 

138.9 

139.8 

140.7 

141.7 

142.6 

143.6 

144-5 

1454 

146.4 

147-3 

31 

148.3 

149-3 

150.2 

151-2 

152.2 

I53-I 

I54-I 

I55-I 

156.1 

157-0 

32 

158.0 

159.0 

160.0 

161.0 

162.0 

163.0 

164.0 

165.0 

166.0 

167.0 

33 

I68.I 

169.1 

170.1 

171.1 

172.2 

173.2 

174.2 

175-3 

176.3 

177-3 

34 

178.4 

179.4 

180.5 

181.6 

182.6 

183.7 

184.7 

185.8 

186.9 

188.0 

35 

iSg.O 

190.1 

191.2 

192.3 

1934 

194.5 

195.6 

196.7 

197.8 

198.9 

36 

2OO.O 

2OI.I 

202.2 

203.3 

104-5 

205.6 

206.7 

207.9 

209.0 

2IO.I 

37 

2II-3 

212.4 

213-6 

214-7 

215-9 

217.0 

218.2 

219.3 

220.5 

221.7 

38 

222.8 

224.0 

225.2 

226.4 

227.6 

228.7 

229.9 

231.1 

232.3 

233-5 

39 

234-7 

235-9 

237.1 

238.3 

239-6 

240.8 

242.0 

243-2 

244-5 

245-7 

40 

246.9 

248.1 

249-4 

250.6 

251-9 

253-1 

2544 

255-6 

256.9 

258.1 

.0 

.1 

.2 

•3            .4 

•5 

.6 

.7 

.8 

•9 

Minus  Corrections  for  — •*-=  ^. 

NOTE. — The  quantities  from  the  above  table  divided  by  two  give  tlie  plus 

corrections  for  -4^-=  -. 
2         4, 


64 
TABLE   No.  12.— LEVEL  CUTTINGS.         -=  l ;  5=18  feet 


& 

.0 

.1 

.2 

-3     -4  |   -5 

§ 

-7     .8  !   .9 

o 

o.o 

6.7 

13-5 

20.3  -   27.3   34.3 

41-3 

48-5 

55-7|   63.0 

I 

70.4 

77-8 

85-3 

92.9   100.6   108.3 

116.1 

124.0 

132.01  140.0 

2 

148.1 

156.3 

164.6 

172.9 

181.3   189.8 

198.4 

207.0  215.7   224.5 

3 

233.3 

242.3 

251.3 

260.3 

269.5 

278.7 

288.0 

297.4  306.8]  316.3 

4 

325.9 

335-6 

345-3 

355-1 

365.0 

375-0 

385-0 

395-1 

405-3 

415.6 

5 

425.9 

436.3 

446.8 

457-4 

468.0 

478-7 

489-5 

500.3 

5II-3 

522.3 

6 

533.3 

544-5 

555-7 

567.0 

578.4 

589-8 

601.3 

612.9!  624.6 

636.3 

7 

648.1 

660.0 

672.0 

684.0 

696.1 

708.3 

720.6 

732.9   745.3 

757-8 

8 

770.4 

•783-0 

795-7 

808.5 

821.3 

834-3 

847-3 

860.3   873.5 

886.7 

9 

900.0 

9134 

926.8 

940-3 

953-9 

967.6 

981.3 

995.  il  1009 

1023 

10 

1037 

1051 

1065 

1080 

1094 

1108 

1123 

H37 

1152 

1167 

ii 

1181 

1196 

1211 

1226 

1241 

1256 

1272 

1287 

1302 

1318 

12 

1333 

1349 

1365 

1380 

1396 

1412 

1428 

1444 

1460 

1476 

13 

1493 

1509 

1525 

1542 

1558 

1575 

1592 

1608 

1625 

1642 

14 

1659 

1676 

1693 

1711 

1728 

1745 

1763 

1780 

1798 

1816 

15 

1833 

1851 

1869 

1887 

1905 

1923 

1941 

1960 

1978 

1996 

16 

2015 

2033 

2O52 

2071 

2089 

2108 

2127 

2146 

2165 

2184 

17 

2204 

2223 

2242 

2262 

2281 

2301 

2321 

2340 

2360 

2380 

18 

2400 

2420 

2440. 

2460 

2481 

2501 

2521 

2542 

2562 

2583 

19 

2604 

2624 

2645 

2666 

2687 

2708 

2729 

2751 

2772 

2793 

20 

2815 

2836 

2858 

2880 

2901 

2923 

2945 

2967 

2989 

3011 

21 

3033 

3056 

3078 

3100 

3123 

3H5 

3168 

3191 

3213 

3236 

22 

3259 

3282 

3305 

3328 

3352 

3375 

3398 

3422 

3445 

3469 

23 

3493 

35i6 

3540 

3564 

3588 

3612 

3636 

3660 

3685 

3709 

24 

3733 

3758 

3782 

3807 

3832 

3856 

3881 

3906 

3931 

3956 

25 

393i 

4007 

4032 

4057 

4083 

4108 

4134 

4160 

4i85 

4211 

26 

4237 

4263 

4289 

4315 

4341 

4368 

4394 

4420 

4447 

4473 

27 

4500 

4527 

4553 

458o 

^07 

4634 

4661 

4688 

4716 

4743 

28 

4770 

4798 

4825 

4853 

4881 

4908 

4936 

4964 

4992 

5020 

29 

5048 

5076 

5105 

5133 

5161 

5190 

5218 

5247 

5276 

5304 

30 

5333 

5362 

5391 

5420 

5449 

5479 

5508 

5537 

5567 

5596 

31 

5626 

5656 

5685 

5715 

5745 

5775 

5805 

5835 

5865 

5896 

32 

5926 

5956 

5987 

6017 

6048 

6079 

6109 

6140 

6171 

6202 

33 

6233 

6264 

6296 

6327 

6358 

6390 

6421 

6453 

6485 

6516 

34 

6548 

6580 

6612 

6644 

6676 

6708 

6741 

6773 

6805 

6838 

35 

6870 

6903 

6936 

6968 

7001 

7034 

7067 

7100 

7133 

7167 

36 

7200 

7233 

7267 

7300 

7334 

7368 

7401 

7435 

7469 

7503 

37 

7537 

7571 

7605- 

7640 

7674 

7708 

7743 

7777 

7812 

7847 

38 

7881 

7916 

7951 

7986 

8021 

8056 

8092 

8127 

8162 

8198 

39 

8233 

8269 

8305 

8340 

8376 

8412 

8448 

8484 

8520 

8556 

40 

8593 

8629 

8665 

8702 

8738 

8775 

8812 

8848 

8885 

8922 

4i 

8959 

8996 

9033 

9071 

9108 

9145 

9183 

9220 

9258 

9296 

42 

9333 

9371 

9409 

9447 

9485 

9523 

956i 

9600 

9638 

9676 

43 

9715 

9753 

9792 

9831 

9869 

9908 

9947 

9986 

10025 

10064 

44 

10104 

10143 

10182 

IO222 

10261 

10301 

10341 

10380 

10420 

10460 

45 

10500 

10540 

10580 

10620 

10661 

10701 

10741 

10782 

10822 

10863 

46 

10904 

10944 

10985 

IIO26 

11067 

11108 

11149 

11191 

11232 

11273 

47 

H3I5 

H356 

11398 

II440 

11481 

U523 

11565 

11607 

11649 

11691 

48 

H733 

11776 

11818 

II860 

11903 

H945 

11988 

12031 

12073 

12116 

49 

12159 

12202 

12245 

12288 

12332 

12375 

12418 

12462 

12505  12549 

50 

12593 

12636 

12680 

12724 

12768 

12812 

12856 

12900 

12945 

12989 

5i 

13033 

13078 

13122 

I3I67 

13212 

13256 

I330I 

T3346 

I3391 

13436 

52 

13481 

13527 

13572 

I36I7 

13663 

13708 

13754 

13800 

13845 

13891 

53  13937 

13983 

14029 

14075 

14121 

14168 

14214 

14260 

14307 

14353 

54)14400 

14447 

14493 

14540 

14587 

14634 

14681 

14728 

14776 

14823 

55 

14870 

I49I8 

14965 

I50I3 

15061 

15108 

15156 

15204 

15252 

15300 

56 

15348 

15396 

15445 

15493 

I554I 

15590 

15638 

15687 

15736 

15784 

57 

15833 

15882 

15931 

15980 

16029 

16079 

16128 

16177 

16227 

16276 

58 

16326 

16376 

16425 

16475 

16525 

16575 

16625 

16675 

16725 

16776 

59 

16826 

16876 

16927 

16977 

17028 

17079 

17129 

17180 

17231 

17282 

60 

17333 

17384 

17436 

17487 

17538 

17590 

17641 

17693 

17745 

17796 

.0 

.1 

.2 

•3 

•4 

•5 

.6 

•7 

.8 

•9 

65 


TABLE  Ko.  13. — LEVEL   CUTTINGS.    -£-=  1 ;  b=Wfcct. 


8+8' 


ta 

.0 

.1 

.2 

•3 

.4 

•5> 

.6 

.7     .8 

•9 

o 

00.0 

II.  I 

22.4 

33-7 

45-0 

56.5 

68.0 

79-6 

91-3 

103.0 

I 

114.8 

126.7 

I3S-7 

150.7 

162.8 

175-0 

187-3 

199.6 

2I2.O 

224.5 

2 

237.0 

249-7 

262.4 

275-1 

288.0 

300.9 

313.9 

327-0 

340.1 

353-4 

3 

366.7 

380.0 

393-5 

407.0 

420.6 

434-3 

448.0 

461.8 

475-7 

489.7 

4 

503.7 

517.8 

532.0 

546.3 

560.6 

575-0 

589-5 

604.0 

618.7 

6334 

5   648.1 

663.0 

677-9 

692.9 

708.0 

723.1 

738.4 

753-7 

76g.c 

7S4.5 

6 

800.0 

815.6 

831-3 

847.0 

862.8 

878.7 

894.7 

910.7 

926.8 

943-0 

7 

959-3 

975-6 

992.0 

1008 

1025 

1042 

1058 

1075 

1092 

1109 

8 

1126 

H43 

1160 

1177 

H95 

1212 

1229 

1247 

1265 

1282 

9 

1300 

1318 

1336 

1354 

1372 

1390 

1408 

1426 

1445 

1463 

10 

1481 

1500 

1519 

1537 

1556 

1575 

1594 

1613 

1632 

1651 

ii 

1670 

1690 

1709 

1728 

1748 

1768 

1787 

1807 

1827 

1847 

12 

1867 

1887 

1907 

1927 

1947 

1968 

1988 

2008 

2029 

2050 

J3 

2070 

2091 

2112 

2133 

2154 

2175 

2196 

2217 

2239 

2260 

14 

2281 

2303 

2325 

2346 

2368 

2390 

2412 

2434 

2456 

2478 

15 

2500 

2522 

2545 

2567 

2589 

26l2 

2635 

2657 

2680 

2703 

16 

2726 

2749 

2772 

2795 

2818' 

2842 

2865 

2888 

2912 

2936 

17 

2959 

2983 

3007 

3031 

3055 

3079 

3103 

3127 

3i5i 

3176 

18 

3200 

3224 

3249 

3274 

3298 

3323 

3348 

3373 

3398 

3423 

19 

3448 

3473 

3499 

3524 

3549 

3575 

3601 

3626 

3652 

3678 

20 

3/04 

3730 

3756 

3782 

3808 

3834 

3861 

3887 

3913 

3940 

21 

3967 

3993 

4020 

4047 

4074 

4101  . 

4128 

4155 

4182 

4210 

22 

4237 

4264 

4292 

4320 

4347 

4375 

4403 

4431 

4459 

4487 

23 

4515 

4543 

4571 

4600 

4628 

4656 

4685 

4714 

4742 

4771 

24 

4800 

4829 

4858 

4887 

4916 

4945 

4975 

5004 

5033 

5063 

25 

5093 

5122 

5152 

5182 

5212 

5242 

5272 

5302 

5332 

5362 

26 

5393 

5423 

5453 

5484 

5515 

5545 

5576 

5607 

5638 

5669 

27 

5700 

5731 

5762 

5794 

5825   5856 

5888 

5920 

5951 

5983 

28 

6015 

6047 

6079 

6111 

6i43   6175 

6207 

6240 

6272 

6304 

29 

6337 

6370 

6402 

6435 

6468 

6501 

6534 

6567 

6600 

6633 

30 

6667 

6700 

6733 

6767 

6801 

6834 

6868 

6902 

6936 

6970 

31 

7004 

7038 

.7072 

7106 

7141 

7175 

7209 

7244 

7279 

7313 

32 

7348 

7383 

7418 

7453 

7483 

7523 

7558 

7594 

7629 

7664 

33 

7700 

7736 

7771 

7807 

7843 

7879 

7915 

7951 

7987 

8023 

34 

8059 

8096 

8132 

8168 

8205 

8242 

8278 

8315 

8352 

8389 

35 

8426 

8463 

8500 

8537 

8575 

8612 

8649 

8687 

8725 

8762 

36 

8800 

8838 

8876 

8914 

8952 

8990 

9028 

9066 

9I05 

9J43 

37 

9181 

9220 

9259- 

9297 

9336 

9375 

9414 

9453 

9492 

9531 

38 

9570 

9610 

9649 

9688 

9728 

9/68 

9807 

9847 

9887 

9927 

39 

9967 

10007 

10047 

10087 

10127 

10168 

10208 

10248 

10289 

10330 

40 

10370 

10411 

10452 

10493 

10534 

10575 

10616 

10657 

10699 

10740 

4i 

10781 

10823 

10865 

10906 

10948 

10990 

11032 

11074 

11116 

11158 

42 

1  1  200 

11242 

11285 

11327 

11369 

11412 

II455 

11497 

11540 

H5S3 

43 

11626 

11669 

11712 

H755 

11798 

11842 

11885 

11928 

11972 

12016 

44  |  i  205  9 

12103 

12147 

12191 

12235 

12279 

12323 

12367 

12411 

12456 

45 

12500 

12544 

12589 

12634 

12678 

12723 

12768 

12813 

12858 

12903 

46 

12948 

12993 

13039 

13084 

13129 

I3I75 

13221 

13266 

13312 

13358 

47 

13404 

13450 

13496 

13542 

13588 

13634 

13681 

13727 

13773 

13820 

48  13867 

139*3 

13960 

14007 

14054 

14101 

14148 

I4I95 

14242 

14290 

49 

14337 

14384 

14432 

14480 

14527 

14575 

14623 

14671 

14719 

14767 

50 

14815 

14863 

14911 

14960 

15008 

15056 

15105 

I5I54 

15202 

15251 

5i 

15300 

15349 

1539s 

15447 

15496 

15545 

15595 

15644 

15693 

15743 

52 

15793 

15842 

15892 

15942 

15992 

16042 

16092 

16142 

16192 

16242 

53 

16293 

16343 

16393 

16444 

16495 

16545 

16596 

16647 

16698 

16749 

54 

16800 

16851 

16902 

16954 

17005 

17056 

17108 

17160 

17211 

17263 

55 

I73I5 

17367 

17419 

17471 

17523 

17575 

17627 

17680 

17732 

17784 

56 

1/837 

17890 

17942 

17995 

18048 

18101 

18154 

18207 

18260 

18313 

57 

18367 

18420 

18473 

18527 

18581 

18634 

18688 

18742 

18796 

18850 

58 

18904 

18958 

19012 

19066 

19121 

I9I75 

19229 

19284 

19339 

19393 

59 

19448 

19503 

19558 

19613 

19668 

19723 

19778 

i9834 

19889 

19944 

60 

2OOOO 

20056 

201  1  1 

20167 

20223 

20279 

20335 

20391 

20447 

20503 

' 

.O      .1 

.2 

•3     -4  i   -5     -6     .7     -8    .9 

66 


TABLE  No. 


Plus  Corrections  for  s-~-  —  1. 


"o 

i 

1 

.0 

,i 

.2 

•3 

•4 

.5 

.6 

• 

•7 

.8 

•9 

O 

o.o 

o.o 

O.O 

o.o 

o.o 

O.I 

O.I 

0.2 

0.2 

0-3 

I 

0.3 

0.4 

0.4 

0-5 

0.6 

0.7 

0.8 

0.9 

I.O 

i.i 

2 

1.2 

1.4 

1-5 

1.6 

1.8 

1.9 

2.1 

2.2 

2.4 

2.6 

3 

2.8 

3-o 

3-2 

3-4 

3-6 

3.8 

4.0 

4.2 

4-5 

4-7 

4 

4-9 

5-2 

5-4 

5-7 

6.0 

6-3 

6-5 

6.8 

7.1 

74 

5 

7-7 

8.0 

8-3 

8-7 

9.0 

9-3 

9-7 

IO.O 

10.4 

10.7 

-6 

ii.  i 

"n-5 

11.9 

12.3 

12.6 

13.0 

13-4 

13-9 

14-3 

14.7 

7 

15-1 

15-6 

16.0 

16.4 

16.9 

17.4 

17.8 

18.3 

18.8 

19-3 

8 

19.8 

20.3 

20.8 

21.3 

21.8 

22.3 

22.8 

23-4 

23-9 

24-4 

9 

25.0 

.25.6 

26.1 

26.7 

27.3 

27-9 

28.4 

29.0 

29.6 

30-3 

10 

30-9 

31-5 

32.1 

32-7 

33-4 

34-0 

34-7 

35-3 

36.0 

36.7 

ii 

37-3 

38.0 

38.7 

39-4 

40.1 

40.8 

4i-5 

42.3 

43-0 

43-7 

12 

44-4 

45-2 

45-9 

46-7 

47-5 

48.2 

49-0 

49.8 

50.6 

51.4 

13 

52.2 

53-0 

53-8 

54-6 

554 

56.2 

57-1 

57-9 

58.8 

59-6 

14 

60.5 

61.4 

62.2 

63.1 

64.0 

64.9 

65.8 

66.7 

67.6 

68.5 

15 

69.4 

70.4 

7i-3 

72.3 

73-2 

74.2 

75-i 

76.1 

77.0 

78.0 

iG 

79.0 

So.o 

Si.o 

82.0 

83.0 

84.0 

85.0 

86.1 

87.1 

88.2 

17 

89.2 

9°-3 

9r-3 

92.4 

934 

94-5 

95-6 

96.7 

97-8 

98.9 

i3 

100.0 

IOI.I 

IO2.2 

103.4 

104.5 

105.6 

106.8 

107.9 

109.1' 

1  10.2 

ID 

111.4 

II2.6 

H3.8 

115.0 

116.2 

117.4 

118.6 

119.8 

I2I.O 

122.2 

20 

123.5 

124.7 

125.9 

127.2 

128.4 

129-7 

131.0 

132.3 

133-5 

134-8 

21 

136.1 

137.4 

138.7 

140.0 

141-3 

142.7 

144.0 

145-3 

146.7 

148.0 

22 

149.4 

150.7 

I52.I 

153-5 

.154-9 

156.3 

157-6 

159.0 

160.4 

161.9 

23 

163.3 

164.7 

I66.I 

167.6 

169.0 

170.4 

171.9 

173-4 

174.8 

176.3 

24 

177.8 

179-3 

180.8 

182.3 

183.8 

185-3 

186.8 

188.3 

lSg.8 

I9I.4 

25 

192.9 

194.4 

196.0 

197.6 

199.1 

200.7 

202.3 

203.9 

2054 

207.0 

26 

208.6 

210.3 

211.9 

213-5 

215.1 

216.7 

218.4 

22O.O 

221.7 

223.3 

27 

225.0 

226.7 

228.3 

230.0 

231.7 

233-4 

235-1 

236.8 

238.5 

240.3 

28 

242.0 

243.7 

245-4 

247-2 

248.9 

250.7 

252.5 

254.2 

256.0 

257.8 

2g 

259.6 

261.4 

263.2 

265.0 

266.8 

268.6 

270.4 

272.2 

274.1 

275-9 

30 

277.8 

279.6 

281.5 

283.4 

285.2 

287.1 

289.0 

290.9 

292.8 

294-7 

31 

296.6 

298.5 

300.4 

302.4 

304-3 

306.3 

308.2 

310.2 

3I2.I 

3I4.I 

32 

316.0 

318.0 

320.0 

322.0 

324.0 

326.0 

328.0 

330.0 

332.0 

334-1 

33 

336.1 

338.2 

340.2 

342.3 

344-3 

346.4 

348.4 

350.5 

352.6 

354-7 

34 

356.8 

358.9 

361.0 

363-1 

365-2 

3674 

369-5 

371.6 

373-8 

375-9 

35 

373.1 

380.2 

382.4 

384-6 

386.8 

389-0 

391.2 

393-4 

395-6 

397-8 

36 

400.0 

402.2 

404-5 

406.7 

408.9 

411.2 

4134 

4I5-7 

418.0 

420.3 

37 

422.5 

424.8 

427.1 

4294 

431-7 

434-0 

436.3 

438.7 

441.0 

443-3 

38 

445-7 

448.0 

450.4 

452.7 

455-1 

457-5 

459-9 

462.3 

464.6 

467.0 

39 

469.4 

471.9 

474-3 

476.7 

479.1 

481.6 

484.0 

486.4 

488.9 

491.4 

40 

493-8 

496.3 

498.8 

501.3 

503-8 

506.2 

508.8 

5II-3 

513.8 

516.3 

.0 

.1 

.2 

•3 

•4 

•5 

.6 

•7 

.8 

•9 

Minus  Corrections  for  -~-  = 


NOTE. — For  minus  corrections  for  ~-  —  jj  gee  Table  5. 


67 

TABLE  No.  15.— LEVEL  CUTTINGS.     *^-=H;&  =  l4/<?rf 


-~&  — 

&. 

.0 

.1 

.2 

•3     -4   |   -5 

.6 

•7 

.8 

•9 

o 

o.o 

5-2 

10.6 

16.1 

21.6 

27-3 

33-i 

39-0 

45-0 

51-2 

I 

574 

63.8 

70.2 

76.8 

83.5 

90-3 

97-2 

104.2 

111.3 

118.6 

2 

125.9 

1334 

141.0 

148.6 

156.4 

164.4 

172.4 

180.5 

188.7 

IQ7-I 

3 

205.6 

214.1 

222.8 

231.6 

240.5 

249-5 

258.7 

267.9 

277-3 

286.7 

4 

296.3 

306.0 

315.8 

325.7 

335-7 

345-8 

356.1 

366.4 

376.9 

387.5 

5 

398.1 

408.9 

419.9 

430.9 

442.0 

453-2 

464.6 

476.1 

487.6 

499-3 

6 

511.1 

523.0 

535-0 

547.2 

5594 

571-8 

584.2 

596.8 

609.5 

622.3 

7 

635-2 

648.2 

661.3 

674.6 

687.9 

701.4 

715.0 

728.6 

742.4 

7564 

8 

770.4 

784.5 

798.7 

813-1 

827.6 

842.1 

856.8 

871.6 

886.5 

901.5 

9 

916.7 

931.9 

947-3 

962.7 

978.3 

994-0 

1010 

1026 

1042 

1058 

10 

1074 

1090 

1167 

1123 

1140 

H57 

1174 

1191 

1208 

1225 

•ii 

1243 

1260 

1278 

1295 

1313 

I33i 

1349 

1367 

1385 

1404 

12 

1422 

1441 

1459 

1478 

1497 

1516 

1535 

1555 

1574 

1593 

13 

1613 

1633 

1652 

1672 

1692 

1713 

1733 

1753 

1774 

1794 

14 

1815 

1836 

1857 

1878 

1899 

1920 

1941 

1963 

1984 

2006 

15 

2028 

2050 

2072 

2094 

2116 

2138 

2161 

2183 

2206 

2229 

16 

2252 

2275 

2298 

2321 

2345 

2368 

2392 

2415 

2439 

2463 

17 

2487 

2511 

2535 

2560 

2584 

2609 

2633 

2658 

2683 

2708 

iS 

2733 

2759 

2784 

2809 

2835 

2861 

2886 

2912 

2938 

2965 

19 

2991 

3017 

3044 

3070 

3097 

3124 

3151 

3178 

3205 

3232 

20 

3259 

3287 

3314 

3342 

3370 

3398 

3426 

3454 

3482 

35io 

21 

3539 

3567 

3596 

3625 

3654 

3683 

3712 

3741 

3771 

3800 

22 

3830 

3359 

3889 

3919 

3949 

3979 

4009 

4040 

4070 

4101 

23 

4131 

4162 

4193 

4224 

4255 

4287 

4318 

4349 

438i 

4413 

24 

4444 

4476 

4508 

4541 

4573 

4605 

4638 

4670 

4703 

4736 

25 

4769 

4802 

4835 

4868 

4901 

4935 

4968 

5002 

5036 

5070 

26 

5104 

5138 

5172 

5206 

5241 

5275 

5310 

5345 

538o 

5415 

27 

5450 

5485 

5521 

5556 

5592 

5627 

5663 

5699 

5735 

577i, 

28 

5807 

5844 

5880 

59J7 

5953 

5990 

6027 

6064 

6101 

6139 

29 

6176 

6213 

6251 

6289 

6326 

6364 

6402 

6441 

6479 

6517 

30 

6556 

6594 

6633 

6672 

6711 

6750 

6789 

6828 

6867 

6907 

31 

6946 

6986 

7026 

7066 

7106 

7146 

7186 

7226 

7267 

7307 

32 

7343 

7389 

7430 

7471 

7512 

7553 

7595 

7636 

7678 

7719 

33 

7761 

7803 

7845 

7887 

7929 

7972 

8014 

8057 

8099 

8142 

34 

8185 

8228 

8271 

8315 

8358 

8401 

8445 

8489 

8532 

8576 

35 

8620 

8665 

8709 

8753 

8798 

8842 

8887 

8932 

8977 

9022 

36 

9067 

9112 

9*57 

9203 

9248 

9294 

9340 

9386 

9432 

9478 

37 

9524 

95/0 

9617 

9663 

9710 

9757 

9804 

9851 

9898 

9945 

38 

9993 

10040 

zooSS 

10135 

10183 

10231 

10279 

10327 

10375 

10424 

39 

10472 

10521 

10569 

10618 

10667 

10716 

10765 

10815 

10864 

10913 

40 

10963 

11013 

11062 

IIII2 

11162 

11213 

11263 

H3I3 

11364 

11414 

41 

11465 

11516 

11567 

Il6l8 

11669 

11720 

11771 

11823 

11874 

11926 

42 

11978 

12030 

12082 

I2I34 

12186 

12238 

12291 

12343 

12396 

12449 

43 

12502 

12555 

12608 

I266I 

12715 

12768 

12822 

12875 

12929 

12983 

44 

13037 

13091 

I3I45 

I32OO 

13254 

13309 

13363 

13418 

13473 

13528 

45 

13583 

13639 

13694 

13749 

13805 

13861 

13916 

13972 

14028 

14085 

46 

14141 

14197 

14254 

I43IO 

14367 

14424 

14481 

14538 

14595 

14652 

47 

14709 

14767 

14824 

14882 

14940 

14998 

15056 

I5H4 

15172 

15230 

48 

15289 

15347 

15406 

15465 

15524 

15583 

15642 

15701 

15761 

15820 

49 

15880 

15939 

J5999 

16059 

16119 

16179 

16239 

16300 

16360 

16421 

50 

16481 

16542 

16603 

16664 

16725 

16787 

16848 

16909 

16971 

17033 

5i 

17094 

17156 

17218 

I728l 

17343 

17405 

17468 

17530 

17593 

17656 

52 

I77I9 

17782 

17845 

17908 

17971 

18035 

18098 

18162 

18226 

18290 

53 

18354 

18418 

18482 

18546 

18611 

18675 

18740 

18805 

18870 

18935 

54 

19000 

19065 

19131 

19196 

19262 

19327 

19393 

T9459 

19525 

I959I 

55 

i9657 

19724 

19790 

19857 

19923 

19990 

20057 

20124 

20191 

20259 

56 

20326 

20393 

20461 

20529 

20596 

20664 

20732 

20801 

20869 

20937 

57 

21006 

21074 

21143 

2I2I2 

21281 

21350 

21419 

21488 

21557 

21627 

58 

21696 

21766 

21836 

21906 

21976 

22046 

22116 

22186 

22257 

22327 

59 

22398 

22469 

22540 

226II 

22682 

22753 

22825 

22896 

22968 

23039 

60 

23111 

23183 

23255 

23327 

23399 

23472 

23544 

23617 

23689  23762  j 

.0   |   .1 

.2     .3 

•4     -5 

.6 

•7   1   -8   i   .9 

63 
TABLE  jSTo.  1C. — LEVEL    CLTTTIXOS.    ^p- =  H ;  Z>  =  2f 


b    -o   j   .1 

.2 

.3 

•4 

•5     -6     .7   j   .8   |   .9 

o    o.o 

9-7 

19-5 

29.4 

39-4 

49-5    59-8   70.1 

80.6 

91.2 

I 

101.9 

II2.6 

123.6 

134.6 

145-7 

156.9 

168.3 

179.8 

I9I-3 

203.0 

2 

214.8 

226.7 

238.7 

250.9 

263.1 

275-5 

287.91  300.5 

313-2 

326.0 

3|  33«-9 

351-9 

365.0 

378.3 

391.6 

405-1 

418.7  432.4 

446.1 

460.1 

4 

474-1 

488.2 

502.4 

516.8 

531.3 

545.8 

560.5 

575-3 

590-2 

605.2 

5 

620.4 

635-6 

651.0 

666.4 

682.0 

697.7 

7i3j5 

729.4 

7454 

761.5 

C 

777-8 

794-1 

810.6 

827.2 

843.9 

860.6 

877* 

894.6 

911.7 

928.9 

7 

946.3 

963.8 

981.3 

'  999.0 

1017 

1035 

1053 

1071 

1089 

H07 

8 

1126 

H45 

Il63 

1182 

I2OI 

I22O 

1239 

1258 

1278 

1297 

9 

1317 

1336 

1356 

1376 

1396 

I4l6 

1436 

1457 

1477 

1498 

10 

1519 

1539 

1560 

1581 

1602 

1624 

1645 

1666 

1688 

1710 

ii 

1732 

1753 

1775 

1798 

1820 

1842 

1865 

1887 

1910 

1933 

12 

1956 

^)79 

2OO2 

2025 

2048 

2072 

2095 

2119 

2143 

2167 

*3 

2191 

2215 

2239 

2264 

2288 

2312 

2337 

2362 

2387 

2412 

14 

2437 

2462 

2488 

2513 

2539 

2564 

2590 

2616 

2642 

2668 

15 

2694 

2721 

2747 

2774 

2801 

2827 

2854 

2881 

2908 

2936 

16 

2963 

2990 

3018 

3046 

3074 

3101 

3129 

3158 

3186 

3214 

17 

3243 

3271 

3300 

3329 

3358 

3387 

3416 

3445 

3474 

3504 

18 

3533 

3563 

3593 

3623 

3653 

3683 

3713 

3744 

3774 

3804 

19 

3835 

3866 

3897 

3928 

3959 

3990 

4022 

4053 

4085 

4Il6 

20 

4148 

4180 

4212 

4244 

4276 

4309 

4341 

4374 

4407 

4439 

21 

4472 

4505 

4538 

4572 

4605 

4638 

4672 

4706 

4740 

4773 

22 

4807 

4842 

4876 

4910 

4945 

4979 

5014 

5049 

5084 

5H9 

23   5154 

5189 

5224 

5260 

5295 

5331 

5367 

5403 

5439 

5475 

24  I  55H 

5548 

5584 

5620 

5657 

5694 

573i 

5768 

5805  . 

5842 

25  1  5880 

5917 

5955 

5992 

6030 

6068 

6106 

6i44 

6182 

6221 

26   6259 

6298 

6337 

6375 

6414 

6453 

6492 

6532 

6571 

6610 

27  ;  6650 

6690 

6730 

6769 

6809 

6850 

6890 

6930 

6971 

7011 

28 

7052 

7093 

7134 

7175 

7216 

7257 

7298 

7340 

738i 

7423 

29  7465 

7507 

7549 

7591 

7633 

7676 

7718 

776o 

7803 

7846 

30 

7889 

7932 

7975 

8018 

8062 

8105 

8149 

8192 

8236 

8280 

3i 

8324 

8368 

8412 

8457 

8501 

8546 

8591 

8635 

8680 

8725 

32  8770 

8816 

8861 

8906 

8952 

8998 

9044 

9089 

9*35 

9182 

33  9223 

92/4 

9321  1  9367 

94U 

946i 

9508 

9555 

9602 

9649 

34  9696 

9744 

9791   9839 

9887 

9935 

9983 

10031  10079 

10128 

35  10176 

10224 

10273  10322 

10371 

10420 

10469 

10518  10568 

10617 

36  10667 

10716 

10766 

10816 

10866 

10916 

10966 

11017 

11067 

iui3 

37  11169 

11219 

11270 

11321 

11372 

11424 

H475 

11526 

"578 

11630 

38:11682 

H733 

11785 

11838 

11890 

11942 

H995 

12047 

I2IOO 

12153 

39  '12206 

12259 

12312 

12365 

12418 

12472 

12525 

12579 

12633 

12687 

40112741 

12795 

12849 

12904 

12958 

13012 

13067 

13122 

I3I77 

13232 

41  13287 

13342 

13393 

13453 

13509 

13564 

13620 

13676  13732 

13788 

42  13844 

13901 

13957 

14014 

14071 

14127 

14184 

14241  14298 

14356 

43  14413 

14470 

14528 

14586 

14644 

14701 

14759 

14818 

14876 

14934 

44(14993 

15051 

15110 

15169 

15228 

15287 

15346 

15405  15464 

15524 

45  15583 

15643 

*5703 

15763 

15823 

15883 

15943 

16004  16064 

16124 

46|i6iS5 

16246 

16307 

16368 

16429 

16490 

16552 

16613  16675 

16736 

47  |i6798 

16860 

16922 

16984 

17046 

17109 

17171 

17234  117297 

17359 

48117422 

17485 

17548 

17612 

17675 

17738 

17802 

17866  17930 

17993 

49  -18057 

18122 

18186 

18250 

18315 

18379 

18444 

18509  18574 

18639 

50  18704 

18769 

18834 

18900 

18965 

19031 

19097 

19163  19229 

19295 

5i  19361 

19428 

19494 

19560 

19627 

19694 

19761 

19828  19895 

19962 

52  20030 

20097 

20165 

20232 

20300 

20368 

20436 

20504  20572 

20641 

53  20709 

20778 

20847 

20915 

20984 

21053 

2II22 

21192  21261 

21330 

54  21400 

21470 

21540 

21609 

21679 

21750 

21820 

21890  21961 

22031 

55  22102 

22173 

22244 

22315 

22386 

22457 

22528 

22600  22671 

22743 

56  22815 

22887 

22959 

23031 

23103 

23176 

23248 

23320  23393 

23466 

57  [23539 

23612 

23685 

23758 

23832 

23905 

23979 

24052  24126 

24200 

58  24274 

24348 

24422 

24497 

24571 

24646 

24721 

24795  24870 

24945 

59  25020 

25096 

25171 

25246 

25322 

25398 

25474 

25549 

25625 

25702 

60  25778 

25854 

25931 

26007 

26084 

26161 

26238 

26315 

26392 

26469 

.0     .1 

.2     .3     .4     -5 

.6 

•7    -8 

•9 

69 


TABLE  No.  17. 

Plus  Corrections  for  - 


s 

fS( 

.0 

.1 

.2 

•3 

•4 

•5 

.6 

•7 

.3      |      , 

0 

o.o 

0.0 

O.O 

0.0 

O.I 

O.I 

0.2 

0.2 

0-3 

0.4 

I 

o-5 

0.6 

0.7 

0.8 

0.9 

1.0 

1.2 

i-3 

i-5 

i-7 

2 

1.9 

2.Q 

2  *"* 

2.4 

2-7 

2.9 

3-1 

3-4 

3-6 

3-9 

3 

4.2 

4-4 

4-7 

5-o 

5-4 

5-7 

6.0 

6-3 

6.7 

7-0 

4 

7-4 

7.8 

8.2 

8.6 

9.0 

9-4 

9.8 

IO.2 

10.7 

ii.  i 

5 

ii.  6 

12.0 

12.5 

13.0 

135 

14.0 

14-5 

15-0 

15.6 

16.1 

6 

16.7 

17.2 

17.8 

18.4 

19.0 

19.6 

2O.2 

20.8 

21.4 

220 

7 

22.7 

23-3 

24.0 

24-7 

25-4 

26.6 

26.7 

27.4 

28.2 

28.9 

8 

29.6 

30.4 

3I-I 

31-9 

32-7 

33-4 

34-2 

35-0 

35-9 

36.7 

9 

37-5 

33.3 

39-2 

40.0 

40.9 

41.8 

42.7 

43-6 

44-5 

45-4 

10 

46.3 

47.2 

48.2 

49.1 

50.1 

51-0 

52. 

53- 

54- 

55- 

ii 

56. 

57- 

58-1 

59-i 

60.2 

61.2 

62.3 

63-4 

64-5 

65.6 

12 

66.7 

67.8 

68.9 

70. 

71.2 

72-3 

73-5 

74-7 

75-9 

77. 

13 

78.2 

79-4 

80.7 

81.9 

83-1 

84.4 

85.6 

86.9 

88.2 

89.4 

14 

90.7 

92.0 

93-4 

94-7 

96.0 

97-3 

93.7 

IOO. 

101.4 

I02.S 

15 

104.2 

105.6 

107.0 

108.4 

109.8 

III.  2 

112.7 

114.1 

115.6 

117. 

16 

118.5 

I2O. 

121.5 

123. 

124-5 

126. 

127.6 

129.1 

I30.7 

132.2 

17 

133-3 

135-4 

137.0 

138.6 

140.2 

I4I.8 

143-4 

145- 

146.7 

148.3 

18 

150. 

I5I.7 

153-4 

155- 

156.7 

158.4 

160.2 

161.9 

163-6 

165.4 

19 

167.1 

168.9 

170.7 

172.4 

174.2 

176.0 

177.9 

179.7 

181.5 

183.3 

20 

185.2 

I87. 

188.9 

190.8 

192.7 

194.6 

196.5 

198.4 

200.3 

2O2.2 

21 

204.2 

206.1 

208.  i 

210. 

212. 

214. 

216. 

218. 

220. 

222. 

22 

224.1 

226.1 

228.2 

230.2 

232.3 

234-4 

236-5 

238.6 

240.7 

242.8 

23 

244.9 

247. 

249.2 

251.3 

253-5 

255-7 

257-9 

260.0 

262.2        264.4 

24 

266.7      268.9 

271.1 

273-4 

275-6 

277.9 

280.2 

282.4 

284.7 

287.0 

25 

289.4 

291.7 

294. 

296.3 

298.7 

301.0 

3034 

305-8 

308.2 

310.6 

25     313. 

315-4 

317.3 

320.2 

322.7 

325-I 

327-6 

330.0 

332-5 

335- 

27     337-5 

340.0 

342.5 

345-0 

347-6 

350.1 

352-7 

355-2 

357-3 

360.4 

28     363.0 

365.6 

368.2 

370.8 

373-4 

376.0 

373.7 

381-3 

384-0 

386.7 

29     3894 

392.0 

394-7 

397-4 

400.2 

402.9 

405.6 

408.4 

411.1 

413-9 

30    416.7 

419.4 

422.2 

425.0 

427-9 

430-7 

433-5 

436.3 

439-2 

442.0 

31     444-9 

447-3 

450.7 

453-6 

456.5 

459-4 

462.3 

465-2 

468.2 

47I.I 

32    474.1 

477-0 

480.0 

483-0 

486.0 

489.0 

492.0 

495-0 

498.1 

501.  T 

33  I  504.2 

507.2 

510-3 

513.4 

5i6.5 

519.6 

522.7 

525-8 

528.9 

532-0 

34!  535-2 

533.3 

541-5 

544-7 

547-9 

551-0 

554-2 

557-4 

560.7 

563.9 

35     567-1 

570.4 

573-6 

576.9 

580.2 

583-4 

586.7 

590-0 

593-4 

596.7 

36    600.0 

603.3 

606.7 

610.0 

6i34 

616.8 

620.2 

623.6 

627.0 

630.4 

37     633.8 

637-2 

640.7 

644.1 

647-6 

651.0 

654.5 

658.0 

661.5 

665.0 

38    668.5 

672.0 

675-6 

679-1 

682.7 

686.2 

689.8 

6934 

697.0 

7OO.6 

39     704-2 

707.8 

711.4 

7i5-o 

718.7 

722.3 

726.0 

729-7 

733-4 

737-0 

40     740.7 

744-4 

748.2 

751-9 

755-6 

759-4 

763.1 

766.9 

770.7 

7744 

.0 

.1 

.2 

•3 

•4 

•5 

.6 

.7 

.8 

•9 

Minus  Corrections  for  -—•  =  ^ 

NOTE. — The  quantities  from  above  table  divided  by  two  give  the  plus  correc- 

s4-s'     3 
tionsfor  -5—=  T 


TABLE  Xo.  18. 
Factors  for  Correction  of  Contents  on  Carves. 


ds<? 

dj-d' 

d*d? 

\*j>* 

dsd' 

in 

Factor. 

in 

Factor. 

in 

Factor.   |  in 

Factor. 

in 

Factor. 

feet. 

feet. 

feet. 

[feet. 

feet. 

I 

.OOO22 

21 

.00452 

41 

.00883 

61 

•01314 

Si 

•01/45 

2 

.00043  . 

22 

.00474 

42 

.00905 

62 

.01336 

82 

.01767 

3 

.00065 

23 

.00496 

43 

.00926 

63 

.01357 

83 

.01788 

4 

.00086 

24 

.00517 

44 

.00948 

64 

•01379 

84 

.01810 

5 

.OOIOS 

25 

•00539 

45 

.00970 

65 

.01400 

85 

.01831 

6 

.OOI29 

26 

.00560 

46 

.00991 

66 

.01422 

86 

.01853 

7 

.00151 

27 

.00582 

47 

.01013 

67 

•01444 

87 

.01875 

8 

.OOI72 

28 

.00603 

48 

.01034 

68 

.01465 

88 

.01896 

9 

.00194 

29 

.00625 

49 

.01056 

69 

.01487 

89 

.01918 

10 

.00215 

30 

.00646 

50 

.01077 

70 

.01508 

90 

.01939 

n 

.00237 

31 

.00668 

51 

.01099 

71 

.01530 

91 

.01961 

12 

.00259 

32 

.00689 

52 

.01120 

72 

•OI55I 

92 

.01982 

13 

.OO28O 

33 

.00711 

53 

.OII42 

73 

•01573 

93 

.02004 

M 

.OO3O2 

34 

.00733 

54 

.01163 

74 

•01594 

94 

.02025 

15 

.00323 

35 

.00754 

55 

.01185 

75 

.01616 

95 

.02047 

16 

•00345 

36 

.00776 

56 

.OI2O7 

76 

.01637 

96 

.02068 

17 

.00366 

37 

.00797 

57 

.01228 

77 

.01659 

97 

.02090 

18 

.00388 

33 

.00819 

58 

.01250 

78 

.01681 

98 

.O2III 

19 

.00409 

39 

.00840 

59 

.01271 

79 

.01702 

99 

.02133 

20 

.00431 

40 

.00862 

60 

.01293 

So 

.01724 

100 

.02155 

,   _J 

S 

5 


The  Construction  of  Tables  of  Contents  of  Level  Cuttings. 

Base  =  b  ;  half  sum  of  side  slopes  =  s. 

For  each  0.1  of  height,  the  second  difference  =  (0.074074+) 

Between  heights  0.0  and  0.1  first  difference  =  —  -~^- 
"       2.7    "    2.8    "  " 

5.4    "   5.5    " 


27 


Contents  for  a  height  of  0.1  =  —  ~ 

2.7  = 
5.4  = 

To  write  out  a  table  of  level  cuttings  progressing  in  height  by  tenths, 
rule  five  columns  carried  to  heights  of  2.  7  when  s  =  1  or  one  of  its 
multiples,  and  to  heights  of  5.4  when  s  =  £  or  one  of  its  odd  multiples. 

Example.  —  (See  portion  of  table  given  below)  b  =  28  ;  s  =  1. 
Here  the  second  difference  —  0.074074-f-  ;  first  difference  between 
heights  0.0  and  0.1  ='10.407407+  ;  between  2.7  and  2.8  =  12.407407+. 

Place  the  heights  from  0.0  to  2.8  in  the  first  column  ;  then  put 
first  difference  10.407407+  in  third  column  opposite  0.0  in  first,  and 
second  difference  0.074074+  immediately  above  the  first  difference. 

As  a  test  for  the  continued  addition  of  the  second  difference,  put 
the  first  difference  12.407407+  in  its  place  in  third  column,  opposite 
2.7  in  first.  Now  add  0.074074+  for  each  0.1  of  height  up  to  2.7, 
taking  care  to  record  the  repeating  fractions  correctly,  and  see  that  the 
last  addition  gives  12.407407+  opposite  2.7.  Then  add  each  amount 
in  third  column  to  the  amount  on  its  left  in  second,  recording  each 
sum  in  the  next  line  below,  and  keeping  the  repeating  fractions  cor 
rect.  The  contents  in  second  column  opposite  2.7  should  be  = 
10&+27s  =  307.0. 

JSToAV  repeat  the  amounts  in  the  second  column  to  the  nearest  tenth, 
placing  them  in  the  fourth  column,  and  as  before  with  regard  to  the 
heights  in  the  first.  From  the  fourth  column,  by  subtraction,  write 
the  first  differences  anew,  to  the  nearest  tenth,  in  the  fifth  column, 
and  opposite  their  respective  positions  in  the  third. 

For  the  remainder  of  the  table,  rule  columns  in  sets  of  threes  ;  the 
first  of  each  set  to  contain  respectively  the  heights  from  2.8  to  5.4,  5.5 
to  8.1,  8.2  to  10.8,  etc.  Then  increase  each  of  the  first  differences  in 
the  5th  column  by  2s  —  2.0,  and  the  first  differences  from  2.8  to  5.4 
are  obtained  for  the  eighth  column.  These  again  increased  by  2.0  give 


the  first  differences  from  5.5  to  8.1  for  the  eleventh  column,  etc.  In 
this  way  the  first  differences  for  the  whole  table  may  be  written  to  one 
place  of  decimals.  Each  first  difference  is  to  be  added  to  the  contents 
opposite  in  the  next  column  on  the  left,  and  the  sum  recorded  in  the 
first  line  below.  With  contents  calculated  by  Formula  C  =  (b+hs) 

i  oo 
li  x  -JT~-  at  intervals  for  tests,  mistakes  are  almosfimpossible. 

To  carry  out  the  table  to  whole  numbers  only,  repeat  the  second 
column  to  the  nearest  whole  number,  get  the  first  differences  to  whole 
numbers  by  subtraction,  and  proceed  in  all  respects  as  above  directed.* 

(i)          (2)  (3)  (4)         (5)        (6)       (7)         (8)       (9)       (10)       (n) 


3 

Contents. 

c 

fca 

a 

c 

Ha 

A 

'c 

„ 

_bc 

0.074074 

C 

5 

UJ 

g 

Q 

tc 

•g 

Q 

K.O 

0.000000 

10.407407 

0 

U 

3 

o 
33 

0 

o 

£ 

& 

0 

p 

ti 

.1 

10.407407 

10.481481 

10.4 

10.5 

2.8 

3194 

12.5 

5-5 

682.4 

14-5 

.2 

20.888888 

10-555555 

20.9 

10.5 

•9 

331.9 

12-5 

.6 

696.9 

14-5 

•3 

31.444444 

10.629629 

314 

10.7 

3-o 

3444 

12.7 

•7 

711.4 

14-7 

4 

42.074074 

10.703703 

42.1- 

10.7 

.1 

357-1 

12.7 

.8 

726.1 

14.7 

•5 

52-777777 

10-777777 

52.8 

10.8 

.2 

369-8 

12.8 

-9 

740.8 

14.8 

.6 

63.555555 

10.851851 

63.6 

10.8 

•3 

382.6 

12.8 

6.0 

755-6 

14-8 

-7 

74.407407 

10.925925 

744 

10.9 

4 

3954 

12.9 

.1 

7704 

14-9 

.8 

85-333333 

II.O 

85.3 

II.O 

•5 

408.3 

13.0 

.2 

785.3 

15-0 

•9 

96.333333 

11.074074 

96.3 

ii.  i 

.6 

421.3 

13.1 

•3 

800.3 

I5-I 

I.O 

107.407407 

11.148148 

107.4 

II.  2 

•7 

4344 

13.2 

4 

815.4 

15.2 

.1 

H8.555555 

11.222222 

118.6 

II.  2 

.8 

447-6 

13.2 

.5 

830.6 

15-2 

.2    [129.777777 

11.296296 

129.8 

II.3 

•9 

460.8 

13-3 

.6 

845-8 

15-3 

.3     141.074074 

11.370370 

141.1 

ii-3 

4-0 

474.1 

13.3 

•  7 

861.1 

15-3 

.4     152.444444 

11.444444 

1524 

H-5 

.1 

4874 

13.5 

.8 

876.4 

15-5 

•5 

163.888888 

II.5I85I8 

163.9 

ii.  5 

.2 

500.9 

13-5 

•9 

891.9 

15-5 

.6 

175.407407 

11.592592 

1754 

n.6 

•3 

5144 

13.6 

7.0 

907.4 

15-6 

.7  '187.0 

n.666666 

187.0 

ii.  7 

4 

528.0 

13.7 

.1 

923-0 

15-7 

..8  1198.666666 

11.740740 

198.7 

H.7 

•5 

541-7 

13-7 

.2 

938.7 

15-7 

•9 

210.407407 

11.814814 

210.4 

n.S 

.6 

5554 

13.8 

.3 

15.8 

2.0 

222.222222 

n.888888 

222.2 

11.9 

•7 

569.2 

13-9 

4 

15.9 

.1 

234.IIIIII 

11.962962 

234-1 

12.0 

.8 

583-1 

14.0 

•5  1 

16.0 

.2 

246.074074 

12.037037 

246.1 

12.0 

•9 

597-1 

14.0 

.6 

16.0 

*} 

258.IIIIII 

I2.IIIIII 

258.1 

12.  1 

5-0 

611.1 

14.1 

•  7 

16.1 

4 

270.222222 

I2.I85I85 

270.2 

12.2 

.1 

625.2 

14.2 

.8 

16.2 

.5 

282.407407 

12.259259 

282.4 

12-3 

.2 

6394 

14.3 

•9 

16.3 

.6 

294.666666 

12-333333 

294.7 

12.3 

•3 

653.7 

14.3 

8.0 

16.3 

2.7 

307.0 

12.407407 

307.0 

124 

4 

668.0 

14.4 

8.1 

1083.0 

16.4 

2.3 

319407407 

3194 

i 

*  In  case  the  second  column  does  not  give  a  whole  number  at  tlie  height  of 
2.7,  it  should  be  carried  out  to  5.4,  or  to  the  requisite  multiple,  of  2.7. 


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